eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
1
866
10.4230/LIPIcs.FSTTCS.2021
article
LIPIcs, Volume 213, FSTTCS 2021, Complete Volume
Bojańczyk, Mikołaj
1
Chekuri, Chandra
2
University of Warsaw, Poland
University of Illinois, Urbana-Champaign, IL, US
LIPIcs, Volume 213, FSTTCS 2021, Complete Volume
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021/LIPIcs.FSTTCS.2021.pdf
LIPIcs, Volume 213, FSTTCS 2021, Complete Volume
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
0:i
0:xvi
10.4230/LIPIcs.FSTTCS.2021.0
article
Front Matter, Table of Contents, Preface, Conference Organization
Bojańczyk, Mikołaj
1
Chekuri, Chandra
2
University of Warsaw, Poland
University of Illinois, Urbana-Champaign, IL, US
Front Matter, Table of Contents, Preface, Conference Organization
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.0/LIPIcs.FSTTCS.2021.0.pdf
Front Matter
Table of Contents
Preface
Conference Organization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
1:1
1:1
10.4230/LIPIcs.FSTTCS.2021.1
article
BQP After 28 Years (Invited Talk)
Aaronson, Scott
1
University of Texas, Austin, TX, USA
I will discuss the now-ancient question of where BQP, Bounded-Error Quantum Polynomial-Time, fits in among classical complexity classes. After reviewing some basics from the 90s, I will discuss the Forrelation problem that I introduced in 2009 to yield an oracle separation between BQP and PH, and the dramatic completion of that program by Ran Raz and Avishay Tal in 2018. I will then discuss very recent work, with William Kretschmer and DeVon Ingram, which leverages the Raz-Tal theorem, along with a new "quantum-aware" random restriction method, to obtain results that illustrate just how differently BQP can behave from BPP. These include oracles relative to which NP^{BQP} ̸ ⊂ BQP^{PH} - solving a 2005 open problem of Lance Fortnow - and conversely, relative to which BQP^{NP} ̸ ⊂ PH^{BQP}; an oracle relative to which 𝖯 = NP and yet BQP ≠ QCMA; an oracle relative to which NP ⊆ BQP yet PH is infinite; an oracle relative to which 𝖯 = NP≠ BQP = PP; and an oracle relative to which PP = PostBQP ̸ ⊂ QMA^{QMA^{…}}. By popular demand, I will also speculate about the status of BQP in the unrelativized world.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.1/LIPIcs.FSTTCS.2021.1.pdf
quantum computing
complexity theory
oracle separations
circuit lower bounds
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
2:1
2:1
10.4230/LIPIcs.FSTTCS.2021.2
article
State Complexity of Population Protocols (Invited Talk)
Esparza, Javier
1
https://orcid.org/0000-0001-9862-4919
Technische Universität München, Germany
Population protocols were introduced by Angluin et al. in 2004 to study the theoretical properties of networks of mobile sensors with very limited computational resources. They have also been proposed as a natural computing model, with molecules, cells, or microorganisms playing the role of sensors.
In a population protocol an arbitrary number of indistinguishable, finite-state agents interact randomly in pairs to collectively decide if their initial global configuration satisfies a given property. The property is formalized as a predicate that maps each initial configuration to an output, 0 or 1. Starting from an initial configuration, the agents eventually agree to the correct output almost surely, and continue producing it forever. The protocol is said to stabilize to the correct output.
It is well known that population protocols can decide exactly the semilinear predicates, or, equivalently, the predicates expressible in Presburger arithmetic. Current research concentrates on investigating the amount of resources needed to decide a given predicate. The standard resources, time and memory, translate for population protocols into expected time to stabilization, usually called parallel runtime, and number of states of each agent. In this talk we concentrate on the latter.
A variant of population protocols allows for a leader, a distinguished finite-state agent that is added to the initial configuration and, intuitively, helps the other agents to organize the computation. In the last years my collaborators and I have obtained upper and lower bounds for the state complexity of population protocols with and without a leader. Define the state complexity of a predicate as the minimal number of states of a protocol that decides the predicate, and STATE(η) as the maximum state complexity of the predicates of size at most η, where predicates are encoded as quantifier-free formulas of Presburger arithmetic with coefficients written in binary. Using techniques from the theory of Petri nets and Vector Addition Systems, we have shown that STATE(η) is polynomially bounded, even for leaderless protocols; this improves on the exponential bound given in 2004 by Angluin and collaborators. We have also proved that STATE(η) ∈ Ω(log log η) for leaderless protocols, even for those deciding very simple predicates of the form x ≥ c for some constant c. In the talk I report on these results, and on two very recent, still unpublished results. Modulo the pending peer-review confirmation, the first result shows the existence of leaderless protocols with a polynomial number of states and linear parallel runtime, and the second, due to Leroux, gives a Ω((log log η)^{1/3}) lower bound for protocols with a leader.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.2/LIPIcs.FSTTCS.2021.2.pdf
Population protocols
state complexity
Petri nets
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
3:1
3:1
10.4230/LIPIcs.FSTTCS.2021.3
article
Approximately Counting Graph Homomorphisms and Retractions (Invited Talk)
Goldberg, Leslie Ann
1
https://orcid.org/0000-0003-1879-6089
University of Oxford, UK
A homomorphism from a graph G to a graph H is a function from the vertices of G to the vertices of H that preserves the edges of G in the sense that every edge of G is mapped to an edge of H. By changing the target graph H, we can capture interesting structures in G. For example, homomorphisms from G to a k-clique H correspond to the proper k-colourings of G. There has been a lot of algorithmic work on the problem of (approximately) counting homomorphisms. The goal is to figure out for which graphs H the problem of approximately counting homomorphisms to H is algorithmically feasible. This talk will survey what is known. Despite much work, there are still plenty of open problems. We will discuss the problem of approximately counting list homomorphisms (where the input specifies, for each vertex of G, the list of vertices of H to which it can be mapped). Because the lists add extra expressibility, it is easier to prove that counting homomorphisms to a particular graph H is intractable. In fact, we have a full trichotomy (joint work with Galanis and Jerrum, 2017). Here, the complexity of homomorphism-counting is related to certain hereditary graph classes. The trichotomy will be explained in the talk - no prior knowledge of the area will be assumed. In more recent work, with Focke and Živn{ý}, we have investigated the complexity of counting retractions to H - this problem falls between homomorphism-counting and list-homomorphism counting. Here we have only a partial classification, which applies to all square-free graphs H. So again, there are plenty of open problems.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.3/LIPIcs.FSTTCS.2021.3.pdf
Graph homomorphisms
counting
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
4:1
4:1
10.4230/LIPIcs.FSTTCS.2021.4
article
Indistinguishability Obfuscation from Well-Founded Assumptions (Invited Talk)
Lin, Huijia (Rachel)
1
Paul G. Allen School of Computer Science & Engineering, University of Washington, Seattle, WA, USA
Indistinguishability obfuscation, introduced by Barak et al. [Crypto 2001], aims to compile programs into unintelligible ones while preserving functionality. It is a fascinating and powerful object that has been shown to enable a host of new cryptographic goals and beyond. However, constructions of indistinguishability obfuscation have remained elusive, with all other proposals relying on heuristics or newly conjectured hardness assumptions. In this work, we show how to construct indistinguishability obfuscation from the subexponential hardness of three well-founded assumptions. We prove the following.
Theorem (Informal) Assume sub-exponential hardness for the following:
- the Learning Parity with Noise (LPN) assumption over general prime fields 𝔽_p with polynomially many LPN samples and error rate 1/k^δ, where k is the dimension of the LPN secret, and δ > 0 is any constant;
- the existence of a Boolean Pseudo-Random Generator (PRG) in NC⁰ with stretch n^(1+τ), where n is the length of the PRG seed, and τ > 0 is any constant;
- the Decision Linear (DLIN) assumption on symmetric bilinear groups of prime order.
Then, (subexponentially secure) indistinguishability obfuscation for all polynomial-size circuits exist.
As a corollary, all cryptographic goals that can be achieved using indistinguishability obfuscation can now be achieved assuming the above three assumptions. This includes fully homomorphic encryption, functional encryption, multiparty non-interactive key-exchange, succinct garbled random access machine, and many others.
This is joint work with Aayush Jain (UCLA and NTT Research) and Amit Sahai (UCLA).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.4/LIPIcs.FSTTCS.2021.4.pdf
Cryptography
indistinguishability obfuscation
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
5:1
5:2
10.4230/LIPIcs.FSTTCS.2021.5
article
The Complexity of Gradient Descent (Invited Talk)
Savani, Rahul
1
https://orcid.org/0000-0003-1262-7831
Department of Computer Science, University of Liverpool, UK
PPAD and PLS are successful classes that capture the complexity of important game-theoretic problems. For example, finding a mixed Nash equilibrium in a bimatrix game is PPAD-complete, and finding a pure Nash equilibrium in a congestion game is PLS-complete. Many important problems, such as solving a Simple Stochastic Game or finding a mixed Nash equilibrium of a congestion game, lie in both classes. It was strongly believed that their intersection, PPAD ∩ PLS, does not have natural complete problems. We show that it does: any problem that lies in both classes can be reduced in polynomial time to the problem of finding a stationary point of a continuously differentiable function on the domain [0,1]². Thus, as PPAD captures problems that can be solved by Lemke-Howson type complementary pivoting algorithms, and PLS captures problems that can be solved by local search, we show that PPAD ∩ PLS exactly captures problems that can be solved by Gradient Descent.
This is joint work with John Fearnley, Paul Goldberg, and Alexandros Hollender. It appeared at STOC'21, where it was given a Best Paper Award [Fearnley et al., 2021].
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.5/LIPIcs.FSTTCS.2021.5.pdf
Computational Complexity
Continuous Optimization
TFNP
PPAD
PLS
CLS
UEOPL
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
6:1
6:22
10.4230/LIPIcs.FSTTCS.2021.6
article
Scheduling in the Secretary Model
Albers, Susanne
1
Janke, Maximilian
1
Department of Computer Science, Technische Universität München, Germany
This paper studies online makespan minimization in the secretary model. Jobs, specified by their processing times, are presented in a uniformly random order. The input size n is known in advance. An online algorithm has to non-preemptively assign each job permanently and irrevocably to one of m parallel and identical machines such that the expected time it takes to process them all, the makespan, is minimized.
We give two deterministic algorithms. First, a straightforward adaptation of the semi-online strategy Light Load [Albers and Hellwig, 2012] provides a very simple approach retaining its competitive ratio of 1.75. A new and sophisticated algorithm is 1.535-competitive. These competitive ratios are not only obtained in expectation but, in fact, for all but a very tiny fraction of job orders.
Classically, online makespan minimization only considers the worst-case order. Here, no competitive ratio below 1.885 for deterministic algorithms and 1.581 using randomization is possible. The best randomized algorithm so far is 1.916-competitive. Our results show that classical worst-case orders are quite rare and pessimistic for many applications.
We complement our results by providing first lower bounds. A competitive ratio obtained on nearly all possible job orders must be at least 1.257. This implies a lower bound of 1.043 for both deterministic and randomized algorithms in the general model.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.6/LIPIcs.FSTTCS.2021.6.pdf
Scheduling
makespan minimization
online algorithm
competitive analysis
lower bound
random-order
secretary problem
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
7:1
7:19
10.4230/LIPIcs.FSTTCS.2021.7
article
One-Way Functions and a Conditional Variant of MKTP
Allender, Eric
1
https://orcid.org/0000-0002-0650-028X
Cheraghchi, Mahdi
2
https://orcid.org/0000-0001-8957-0306
Myrisiotis, Dimitrios
3
https://orcid.org/0000-0001-9585-1227
Tirumala, Harsha
1
https://orcid.org/0000-0002-4600-3675
Volkovich, Ilya
4
https://orcid.org/0000-0002-7616-0751
Department of Computer Science, Rutgers University, Piscataway, NJ, USA
Department of EECS, University of Michigan, Ann Arbor, MI, USA
Department of Computing, Imperial College London, London, UK
Computer Science Department, Boston College, Chestnut Hill, MA, USA
One-way functions (OWFs) are central objects of study in cryptography and computational complexity theory. In a seminal work, Liu and Pass (FOCS 2020) proved that the average-case hardness of computing time-bounded Kolmogorov complexity is equivalent to the existence of OWFs. It remained an open problem to establish such an equivalence for the average-case hardness of some natural NP-complete problem. In this paper, we make progress on this question by studying a conditional variant of the Minimum KT-complexity Problem (MKTP), which we call McKTP, as follows.
1) First, we prove that if McKTP is average-case hard on a polynomial fraction of its instances, then there exist OWFs.
2) Then, we observe that McKTP is NP-complete under polynomial-time randomized reductions.
3) Finally, we prove that the existence of OWFs implies the nontrivial average-case hardness of McKTP. Thus the existence of OWFs is inextricably linked to the average-case hardness of this NP-complete problem. In fact, building on recently-announced results of Ren and Santhanam [Rahul Ilango et al., 2021], we show that McKTP is hard-on-average if and only if there are logspace-computable OWFs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.7/LIPIcs.FSTTCS.2021.7.pdf
Kolmogorov complexity
KT Complexity
Minimum KT-complexity Problem
MKTP
Conditional KT Complexity
Minimum Conditional KT-complexity Problem
McKTP
one-way functions
OWFs
average-case hardness
pseudorandom generators
PRGs
pseudorandom functions
PRFs
distinguishers
learning algorithms
NP-completeness
reductions
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
8:1
8:23
10.4230/LIPIcs.FSTTCS.2021.8
article
Generalizations of Length Limited Huffman Coding for Hierarchical Memory Settings
Banchhor, Shashwat
1
Gajjala, Rishikesh
2
1
Sabharwal, Yogish
3
Sen, Sandeep
4
1
Department of Computer Science, Indian Institute of Technology, New Delhi, India
Indian Institute of Science, Bangalore, India
IBM Research, New Delhi, India
Department of Computer Science, Shiv Nadar University, Uttar Pradesh, India
In this paper, we study the problem of designing prefix-free encoding schemes having minimum average code length that can be decoded efficiently under a decode cost model that captures memory hierarchy induced cost functions. We also study a special case of this problem that is closely related to the length limited Huffman coding (LLHC) problem; we call this the soft-length limited Huffman coding problem. In this version, there is a penalty associated with each of the n characters of the alphabet whose encodings exceed a specified bound D(≤ n) where the penalty increases linearly with the length of the encoding beyond D. The goal of the problem is to find a prefix-free encoding having minimum average code length and total penalty within a pre-specified bound P. This generalizes the LLHC problem. We present an algorithm to solve this problem that runs in time O(nD). We study a further generalization in which the penalty function and the objective function can both be arbitrary monotonically non-decreasing functions of the codeword length. We provide dynamic programming based exact and PTAS algorithms for this setting.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.8/LIPIcs.FSTTCS.2021.8.pdf
Approximation algorithms
Hierarchical memory
Prefix free codes
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
9:1
9:14
10.4230/LIPIcs.FSTTCS.2021.9
article
Approximation Algorithms for Flexible Graph Connectivity
Boyd, Sylvia
1
Cheriyan, Joseph
2
Haddadan, Arash
3
Ibrahimpur, Sharat
2
https://orcid.org/0000-0002-1575-9648
School of Electrical Engineering and Computer Science, University of Ottawa, Canada
Department of Combinatorics and Optimization, University of Waterloo, Canada
Warner Music Group, New York, NY, USA
We present approximation algorithms for several network design problems in the model of Flexible Graph Connectivity (Adjiashvili, Hommelsheim and Mühlenthaler, "Flexible Graph Connectivity", Math. Program. pp. 1-33 (2021), IPCO 2020: pp. 13-26). In an instance of the Flexible Graph Connectivity (FGC) problem, we have an undirected connected graph G = (V,E), a partition of E into a set of safe edges S and a set of unsafe edges U, and nonnegative costs {c_e}_{e ∈ E} on the edges. A subset F ⊆ E of edges is feasible for FGC if for any unsafe edge e ∈ F ∩ U, the subgraph (V,F⧵{e}) is connected. The algorithmic goal is to find a (feasible) solution F that minimizes c(F) = ∑_{e ∈ F} c_e. We present a simple 2-approximation algorithm for FGC via a reduction to the minimum-cost r-out 2-arborescence problem. This improves upon the 2.527-approximation algorithm of Adjiashvili et al.
For integers p ≥ 1 and q ≥ 0, the (p,q)-FGC problem is a generalization of FGC where we seek a minimum-cost subgraph H = (V,F) that remains p-edge connected against the failure of any set of at most q unsafe edges; that is, for any set F' ⊆ U with |F'| ≤ q, H-F' = (V, F ⧵ F') should be p-edge connected. Note that FGC corresponds to the (1,1)-FGC problem. We give approximation algorithms for two important special cases of (p,q)-FGC: (a) Our 2-approximation algorithm for FGC extends to a (k+1)-approximation algorithm for the (1,k)-FGC problem. (b) We present a 4-approximation algorithm for the (k,1)-FGC problem.
For the unweighted FGC problem, where each edge has unit cost, we give a 16/11-approximation algorithm. This improves on the result of Adjiashvili et al. for this problem.
The (p,q)-FGC model with p = 1 or q ≤ 1 can be cast as the Capacitated k-Connected Subgraph problem which is a special case of the well-known Capacitated Network Design problem. We denote the former problem by Cap-k-ECSS. An instance of this problem consists of an undirected graph G = (V,E), nonnegative integer edge-capacities {u_e}_{e ∈ E}, nonnegative edge-costs {c_e}_{e ∈ E}, and a positive integer k. The goal is to find a minimum-cost edge-set F ⊆ E such that every (non-trivial) cut of the capacitated subgraph H(V,F,u) has capacity at least k. We give a min(k, 2max_{e ∈ E} u_e)-approximation algorithm for this problem.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.9/LIPIcs.FSTTCS.2021.9.pdf
Approximation Algorithms
Combinatorial Optimization
Network Design
Edge-Connectivity of Graphs
Reliability of Networks
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
10:1
10:22
10.4230/LIPIcs.FSTTCS.2021.10
article
Tight Chang’s-Lemma-Type Bounds for Boolean Functions
Chakraborty, Sourav
1
Mande, Nikhil S.
2
Mittal, Rajat
3
Molli, Tulasimohan
4
Paraashar, Manaswi
1
Sanyal, Swagato
5
Indian Statistical Institute, Kolkata, India
CWI, Amsterdam, The Netherlands
Indian Institute of Technology, Kanpur, India
Tata Institute of Fundamental Research, Mumbai, India
Indian Institute of Technology, Kharagpur, India
Chang’s lemma (Duke Mathematical Journal, 2002) is a classical result in mathematics, with applications spanning across additive combinatorics, combinatorial number theory, analysis of Boolean functions, communication complexity and algorithm design. For a Boolean function f that takes values in {-1, 1} let r(f) denote its Fourier rank (i.e., the dimension of the span of its Fourier support). For each positive threshold t, Chang’s lemma provides a lower bound on δ(f) := Pr[f(x) = -1] in terms of the dimension of the span of its characters with Fourier coefficients of magnitude at least 1/t. In this work we examine the tightness of Chang’s lemma with respect to the following three natural settings of the threshold:
- the Fourier sparsity of f, denoted k(f),
- the Fourier max-supp-entropy of f, denoted k'(f), defined to be the maximum value of the reciprocal of the absolute value of a non-zero Fourier coefficient,
- the Fourier max-rank-entropy of f, denoted k''(f), defined to be the minimum t such that characters whose coefficients are at least 1/t in magnitude span a r(f)-dimensional space. In this work we prove new lower bounds on δ(f) in terms of the above measures. One of our lower bounds, δ(f) = Ω(r(f)²/(k(f) log² k(f))), subsumes and refines the previously best known upper bound r(f) = O(√{k(f)}log k(f)) on r(f) in terms of k(f) by Sanyal (Theory of Computing, 2019). We improve upon this bound and show r(f) = O(√{k(f)δ(f)}log k(f)). Another lower bound, δ(f) = Ω(r(f)/(k''(f) log k(f))), is based on our improvement of a bound by Chattopadhyay, Hatami, Lovett and Tal (ITCS, 2019) on the sum of absolute values of level-1 Fourier coefficients in terms of 𝔽₂-degree. We further show that Chang’s lemma for the above-mentioned choices of the threshold is asymptotically outperformed by our bounds for most settings of the parameters involved.
Next, we show that our bounds are tight for a wide range of the parameters involved, by constructing functions witnessing their tightness. All the functions we construct are modifications of the Addressing function, where we replace certain input variables by suitable functions. Our final contribution is to construct Boolean functions f for which our lower bounds asymptotically match δ(f), and for any choice of the threshold t, the lower bound obtained from Chang’s lemma is asymptotically smaller than δ(f).
Our results imply more refined deterministic one-way communication complexity upper bounds for XOR functions. Given the wide-ranging application of Chang’s lemma to areas like additive combinatorics, learning theory and communication complexity, we strongly feel that our refinements of Chang’s lemma will find many more applications.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.10/LIPIcs.FSTTCS.2021.10.pdf
Analysis of Boolean functions
Chang’s lemma
Parity decision trees
Fourier dimension
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
11:1
11:23
10.4230/LIPIcs.FSTTCS.2021.11
article
Approximate Trace Reconstruction via Median String (In Average-Case)
Chakraborty, Diptarka
1
Das, Debarati
2
Krauthgamer, Robert
3
National University of Singapore, Singapore
Basic Algorithm Research Copenhagen (BARC), University of Copenhagen, Denmark
Weizmann Institute of Science, Rehovot, Israel
We consider an approximate version of the trace reconstruction problem, where the goal is to recover an unknown string s ∈ {0,1}ⁿ from m traces (each trace is generated independently by passing s through a probabilistic insertion-deletion channel with rate p). We present a deterministic near-linear time algorithm for the average-case model, where s is random, that uses only three traces. It runs in near-linear time Õ(n) and with high probability reports a string within edit distance Õ(p² n) from s, which significantly improves over the straightforward bound of O(pn).
Technically, our algorithm computes a (1+ε)-approximate median of the three input traces. To prove its correctness, our probabilistic analysis shows that an approximate median is indeed close to the unknown s. To achieve a near-linear time bound, we have to bypass the well-known dynamic programming algorithm that computes an optimal median in time O(n³).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.11/LIPIcs.FSTTCS.2021.11.pdf
Trace Reconstruction
Approximation Algorithms
Edit Distance
String Median
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
12:1
12:21
10.4230/LIPIcs.FSTTCS.2021.12
article
Approximating the Center Ranking Under Ulam
Chakraborty, Diptarka
1
Gajjar, Kshitij
1
Jha, Agastya Vibhuti
2
National University of Singapore, Singapore
EPFL, Lausanne, Switzerland
We study the problem of approximating a center under the Ulam metric. The Ulam metric, defined over a set of permutations over [n], is the minimum number of move operations (deletion plus insertion) to transform one permutation into another. The Ulam metric is a simpler variant of the general edit distance metric. It provides a measure of dissimilarity over a set of rankings/permutations. In the center problem, given a set of permutations, we are asked to find a permutation (not necessarily from the input set) that minimizes the maximum distance to the input permutations. This problem is also referred to as maximum rank aggregation under Ulam. So far, we only know of a folklore 2-approximation algorithm for this NP-hard problem. Even for constantly many permutations, we do not know anything better than an exhaustive search over all n! permutations.
In this paper, we achieve a (3/2 - 1/(3m))-approximation of the Ulam center in time n^O(m² ln m), for m input permutations over [n]. We therefore get a polynomial time bound while achieving better than a 3/2-approximation for constantly many permutations. This problem is of special interest even for constantly many permutations because under certain dissimilarity measures over rankings, even for four permutations, the problem is NP-hard.
In proving our result, we establish a surprising connection between the approximate Ulam center problem and the closest string with wildcards problem (the center problem over the Hamming metric, allowing wildcards). We further study the closest string with wildcards problem and show that there cannot exist any (2-ε)-approximation algorithm (for any ε > 0) for it unless 𝖯 = NP. This inapproximability result is in sharp contrast with the same problem without wildcards, where we know of a PTAS.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.12/LIPIcs.FSTTCS.2021.12.pdf
Center Problem
Ulam Metric
Edit Distance
Closest String
Approximation Algorithms
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
13:1
13:16
10.4230/LIPIcs.FSTTCS.2021.13
article
Towards Stronger Counterexamples to the Log-Approximate-Rank Conjecture
Chattopadhyay, Arkadev
1
Garg, Ankit
2
Sherif, Suhail
3
Tata Institute of Fundamental Research, Mumbai, India
Microsoft Research India, Bengaluru, India
Vector Institute, Toronto, Canada
We give improved separations for the query complexity analogue of the log-approximate-rank conjecture i.e. we show that there are a plethora of total Boolean functions on n input bits, each of which has approximate Fourier sparsity at most O(n³) and randomized parity decision tree complexity Θ(n). This improves upon the recent work of Chattopadhyay, Mande and Sherif [Chattopadhyay et al., 2020] both qualitatively (in terms of designing a large number of examples) and quantitatively (shrinking the gap from quartic to cubic). We leave open the problem of proving a randomized communication complexity lower bound for XOR compositions of our examples. A linear lower bound would lead to new and improved refutations of the log-approximate-rank conjecture. Moreover, if any of these compositions had even a sub-linear cost randomized communication protocol, it would demonstrate that randomized parity decision tree complexity does not lift to randomized communication complexity in general (with the XOR gadget).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.13/LIPIcs.FSTTCS.2021.13.pdf
Approximate Rank
Randomized Parity Decision Trees
Randomized Communication Complexity
XOR functions
Subspace Designs
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
14:1
14:15
10.4230/LIPIcs.FSTTCS.2021.14
article
Functional Lower Bounds for Restricted Arithmetic Circuits of Depth Four
Chillara, Suryajith
1
CSTAR, International Institute of Information Technology, Hyderabad, India
Recently, Forbes, Kumar and Saptharishi [CCC, 2016] proved that there exists an explicit d^{O(1)}-variate and degree d polynomial P_{d} ∈ VNP such that if any depth four circuit C of bounded formal degree d which computes a polynomial of bounded individual degree O(1), that is functionally equivalent to P_d, then C must have size 2^Ω(√dlog{d}).
The motivation for their work comes from Boolean Circuit Complexity. Based on a characterization for ACC⁰ circuits by Yao [FOCS, 1985] and Beigel and Tarui [CC, 1994], Forbes, Kumar and Saptharishi [CCC, 2016] observed that functions in ACC⁰ can also be computed by algebraic Σ∧ΣΠ circuits (i.e., circuits of the form - sums of powers of polynomials) of 2^(log^O(1) n) size. Thus they argued that a 2^{ω(polylog n)} "functional" lower bound for an explicit polynomial Q against Σ∧ΣΠ circuits would imply a lower bound for the "corresponding Boolean function" of Q against non-uniform ACC⁰. In their work, they ask if their lower bound be extended to Σ∧ΣΠ circuits.
In this paper, for large integers n and d such that ω(log²n) ≤ d ≤ n^{0.01}, we show that any Σ∧ΣΠ circuit of bounded individual degree at most O(d/k²) that functionally computes Iterated Matrix Multiplication polynomial IMM_{n,d} (∈ VP) over {0,1}^{n²d} must have size n^Ω(k). Since Iterated Matrix Multiplication IMM_{n,d} over {0,1}^{n²d} is functionally in GapL, improvement of the afore mentioned lower bound to hold for quasipolynomially large values of individual degree would imply a fine-grained separation of ACC⁰ from GapL.
For the sake of completeness, we also show a syntactic size lower bound against any Σ∧ΣΠ circuit computing IMM_{n,d} (for the same regime of d) which is tight over large fields. Like Forbes, Kumar and Saptharishi [CCC, 2016], we too prove lower bounds against circuits of bounded formal degree which functionally compute IMM_{n,d}, for a slightly larger range of individual degree.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.14/LIPIcs.FSTTCS.2021.14.pdf
Functional Lower Bounds
Boolean Circuit Lower Bounds
Depth Four
Connections to Boolean Complexity
Iterated Matrix Multiplication
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
15:1
15:16
10.4230/LIPIcs.FSTTCS.2021.15
article
On (Simple) Decision Tree Rank
Dahiya, Yogesh
1
Mahajan, Meena
1
https://orcid.org/0000-0002-9116-4398
The Institute of Mathematical Sciences (HBNI), Chennai, India
In the decision tree computation model for Boolean functions, the depth corresponds to query complexity, and size corresponds to storage space. The depth measure is the most well-studied one, and is known to be polynomially related to several non-computational complexity measures of functions such as certificate complexity. The size measure is also studied, but to a lesser extent. Another decision tree measure that has received very little attention is the minimal rank of the decision tree, first introduced by Ehrenfeucht and Haussler in 1989. This measure is not polynomially related to depth, and hence it can reveal additional information about the complexity of a function. It is characterised by the value of a Prover-Delayer game first proposed by Pudlák and Impagliazzo in the context of tree-like resolution proofs. In this paper we study this measure further. We obtain upper and lower bounds on rank in terms of (variants of) certificate complexity. We also obtain upper and lower bounds on the rank for composed functions in terms of the depth of the outer function and the rank of the inner function. We compute the rank exactly for several natural functions and use them to show that all the bounds we have obtained are tight. We also observe that the size-rank relationship for decision trees, obtained by Ehrenfeucht and Haussler, is tight upto constant factors.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.15/LIPIcs.FSTTCS.2021.15.pdf
Boolean functions
Decision trees
certificate complexity
rank
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
16:1
16:16
10.4230/LIPIcs.FSTTCS.2021.16
article
Reachability and Matching in Single Crossing Minor Free Graphs
Datta, Samir
1
Gupta, Chetan
2
Jain, Rahul
3
https://orcid.org/0000-0002-8567-9475
Mukherjee, Anish
4
https://orcid.org/0000-0002-5857-9778
Sharma, Vimal Raj
5
Tewari, Raghunath
5
Chennai Mathematical Institute, Chennai, India
Aalto University, Finland
Fernuniversität in Hagen, Germany
Institute of Informatics, University of Warsaw, Poland
Indian Institute of Technology, Kanpur, India
We show that for each single crossing graph H, a polynomially bounded weight function for all H-minor free graphs G can be constructed in logspace such that it gives nonzero weights to all the cycles in G. This class of graphs subsumes almost all classes of graphs for which such a weight function is known to be constructed in logspace. As a consequence, we obtain that for the class of H-minor free graphs where H is a single crossing graph, reachability can be solved in UL, and bipartite maximum matching can be solved in SPL, which are small subclasses of the parallel complexity class NC. In the restrictive case of bipartite graphs, our maximum matching result improves upon the recent result of Eppstein and Vazirani [David Eppstein and Vijay V. Vazirani, 2021], where they show an NC bound for constructing perfect matching in general single crossing minor free graphs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.16/LIPIcs.FSTTCS.2021.16.pdf
Reachability
Matching
Logspace
Single-crossing minor free graphs
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
17:1
17:10
10.4230/LIPIcs.FSTTCS.2021.17
article
Approximating the Number of Prime Factors Given an Oracle to Euler’s Totient Function
Du, Yang
1
Volkovich, Ilya
2
https://orcid.org/0000-0002-7616-0751
Departments of EECS, CSE Division, University of Michigan, Ann Arbor, MI, USA
Computer Science Department, Boston College, Chestnut Hill, MA, USA
In this work we devise the first efficient deterministic algorithm for approximating ω(N) - the number of prime factors of an integer N ∈ ℕ, given in addition oracle access to Euler’s Totient function Φ(⋅). We also show that the algorithm can be extended to handle a more general class of additive functions that "depend solely on the exponents in the prime factorization of an integer". In particular, our result gives the first algorithm that approximates ω(N) without necessarily factoring N. Indeed, all the previously known algorithms for computing or even approximating ω(N) entail factorization of N, and therefore are either randomized [M. O. Rabin, 1980; D. L. Long, 1981] or require the Generalized Riemann Hypothesis (GRH) [G. L. Miller, 1976].
Our approach combines an application of Coppersmith’s method for finding non-trivial factors of integers whose prime factors satisfy certain "relative size" conditions of [F. Morain et al., 2018], together with a new upper bound on Φ(N) in terms of ω(N) which could be of independent interest.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.17/LIPIcs.FSTTCS.2021.17.pdf
Euler’s Totient Function
Integer Factorization
Number of Prime Factors
Derandomization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
18:1
18:17
10.4230/LIPIcs.FSTTCS.2021.18
article
Fully Dynamic Algorithms for Knapsack Problems with Polylogarithmic Update Time
Eberle, Franziska
1
https://orcid.org/0000-0001-8636-9711
Megow, Nicole
1
https://orcid.org/0000-0002-3531-7644
Nölke, Lukas
1
https://orcid.org/0000-0003-0523-0668
Simon, Bertrand
2
https://orcid.org/0000-0002-2565-1163
Wiese, Andreas
3
https://orcid.org/0000-0003-3705-016X
Faculty of Mathematics and Computer Science, University of Bremen, Germany
IN2P3 Computing Center, CNRS, Villeurbanne, France
Department of Industrial Engineering, University of Chile, Santiago, Chile
Knapsack problems are among the most fundamental problems in optimization. In the Multiple Knapsack problem, we are given multiple knapsacks with different capacities and items with values and sizes. The task is to find a subset of items of maximum total value that can be packed into the knapsacks without exceeding the capacities. We investigate this problem and special cases thereof in the context of dynamic algorithms and design data structures that efficiently maintain near-optimal knapsack solutions for dynamically changing input. More precisely, we handle the arrival and departure of individual items or knapsacks during the execution of the algorithm with worst-case update time polylogarithmic in the number of items. As the optimal and any approximate solution may change drastically, we maintain implicit solutions and support polylogarithmic time query operations that can return the computed solution value and the packing of any given item.
While dynamic algorithms are well-studied in the context of graph problems, there is hardly any work on packing problems (and generally much less on non-graph problems). Motivated by the theoretical interest in knapsack problems and their practical relevance, our work bridges this gap.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.18/LIPIcs.FSTTCS.2021.18.pdf
Fully dynamic algorithms
knapsack problem
approximation schemes
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
19:1
19:13
10.4230/LIPIcs.FSTTCS.2021.19
article
Largest Similar Copies of Convex Polygons in Polygonal Domains
Eom, Taekang
1
Lee, Seungjun
1
Ahn, Hee-Kap
2
https://orcid.org/0000-0001-7177-1679
Department of Computer Science and Engineering, Pohang University of Science and Technology, South Korea
Department of Computer Science and Engineering, Graduate School of Artificial Intelligence, Pohang University of Science and Technology, South Korea
Given a convex polygon with k vertices and a polygonal domain consisting of polygonal obstacles with n vertices in total in the plane, we study the optimization problem of finding a largest similar copy of the polygon that can be placed in the polygonal domain without intersecting the obstacles. We present an upper bound O(k²n²λ₄(k)) on the number of combinatorial changes occurred to the underlying structure during the rotation of the polygon, together with an O(k²n²λ₄(k)log n)-time deterministic algorithm for the problem. This improves upon the previously best known results by Chew and Kedem [SoCG89, CGTA93] and Sharir and Toledo [SoCG91, CGTA94] on the problem in more than 27 years. Our result also improves the time complexity of the high-clearance motion planning algorithm by Chew and Kedem.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.19/LIPIcs.FSTTCS.2021.19.pdf
Polygon placement
Largest similar copy
Polygonal domain
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
20:1
20:21
10.4230/LIPIcs.FSTTCS.2021.20
article
A Faster Algorithm for Finding Closest Pairs in Hamming Metric
Esser, Andre
1
Kübler, Robert
2
Zweydinger, Floyd
3
Cryptography Research Center, Technology Innovation Institute, Abu Dhabi, UAE
Metro AG, Düsseldorf, Germany
Ruhr Universität Bochum, Germany
We study the Closest Pair Problem in Hamming metric, which asks to find the pair with the smallest Hamming distance in a collection of binary vectors. We give a new randomized algorithm for the problem on uniformly random input outperforming previous approaches whenever the dimension of input points is small compared to the dataset size. For moderate to large dimensions, our algorithm matches the time complexity of the previously best-known locality sensitive hashing based algorithms. Technically our algorithm follows similar design principles as Dubiner (IEEE Trans. Inf. Theory 2010) and May-Ozerov (Eurocrypt 2015). Besides improving the time complexity in the aforementioned areas, we significantly simplify the analysis of these previous works. We give a modular analysis, which allows us to investigate the performance of the algorithm also on non-uniform input distributions. Furthermore, we give a proof of concept implementation of our algorithm which performs well in comparison to a quadratic search baseline. This is the first step towards answering an open question raised by May and Ozerov regarding the practicability of algorithms following these design principles.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.20/LIPIcs.FSTTCS.2021.20.pdf
closest pair problem
LSH
nearest neighbor
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
21:1
21:16
10.4230/LIPIcs.FSTTCS.2021.21
article
ETH Tight Algorithms for Geometric Intersection Graphs: Now in Polynomial Space
Fomin, Fedor V.
1
Golovach, Petr A.
1
Inamdar, Tanmay
1
Saurabh, Saket
2
1
University of Bergen, Norway
The Institute of Mathematical Sciences, HBNI, Chennai, India
De Berg et al. in [SICOMP 2020] gave an algorithmic framework for subexponential algorithms on geometric graphs with tight (up to ETH) running times. This framework is based on dynamic programming on graphs of weighted treewidth resulting in algorithms that use super-polynomial space. We introduce the notion of weighted treedepth and use it to refine the framework of de Berg et al. for obtaining polynomial space (with tight running times) on geometric graphs. As a result, we prove that for any fixed dimension d ≥ 2 on intersection graphs of similarly-sized fat objects many well-known graph problems including Independent Set, r-Dominating Set for constant r, Cycle Cover, Hamiltonian Cycle, Hamiltonian Path, Steiner Tree, Connected Vertex Cover, Feedback Vertex Set, and (Connected) Odd Cycle Transversal are solvable in time 2^𝒪(n^{1-1/d}) and within polynomial space.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.21/LIPIcs.FSTTCS.2021.21.pdf
Subexponential Algorithms
Geometric Intersection Graphs
Treedepth
Treewidth
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
22:1
22:19
10.4230/LIPIcs.FSTTCS.2021.22
article
On Fair and Efficient Allocations of Indivisible Public Goods
Garg, Jugal
1
Kulkarni, Pooja
1
Murhekar, Aniket
1
University of Illinois, Urbana-Champaign, IL, USA
We study fair allocation of indivisible public goods subject to cardinality (budget) constraints. In this model, we have n agents and m available public goods, and we want to select k ≤ m goods in a fair and efficient manner. We first establish fundamental connections between the models of private goods, public goods, and public decision making by presenting polynomial-time reductions for the popular solution concepts of maximum Nash welfare (MNW) and leximin. These mechanisms are known to provide remarkable fairness and efficiency guarantees in private goods and public decision making settings. We show that they retain these desirable properties even in the public goods case. We prove that MNW allocations provide fairness guarantees of Proportionality up to one good (Prop1), 1/n approximation to Round Robin Share (RRS), and the efficiency guarantee of Pareto Optimality (PO). Further, we show that the problems of finding MNW or leximin-optimal allocations are NP-hard, even in the case of constantly many agents, or binary valuations. This is in sharp contrast to the private goods setting that admits polynomial-time algorithms under binary valuations. We also design pseudo-polynomial time algorithms for computing an exact MNW or leximin-optimal allocation for the cases of (i) constantly many agents, and (ii) constantly many goods with additive valuations. We also present an O(n)-factor approximation algorithm for MNW which also satisfies RRS, Prop1, and 1/2-Prop.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.22/LIPIcs.FSTTCS.2021.22.pdf
Public goods
Nash welfare
Leximin
Proportionality
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
23:1
23:15
10.4230/LIPIcs.FSTTCS.2021.23
article
Time Space Optimal Algorithm for Computing Separators in Bounded Genus Graphs
Gupta, Chetan
1
Jain, Rahul
2
https://orcid.org/0000-0002-8567-9475
Tewari, Raghunath
3
Aalto University, Finland
Fernuniversität in Hagen, Germany
Indian Institute of Technology Kanpur, India
A graph separator is a subset of vertices of a graph whose removal divides the graph into small components. Computing small graph separators for various classes of graphs is an important computational task. In this paper, we present a polynomial-time algorithm that uses O(g^{1/2} n^{1/2} log n)-space to find an O(g^{1/2} n^{1/2})-sized separator of a graph having n vertices and embedded on an orientable surface of genus g.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.23/LIPIcs.FSTTCS.2021.23.pdf
Graph algorithms
space-bounded algorithms
surface embedded graphs
reachability
Euler genus
algorithmic graph theory
computational complexity theory
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
24:1
24:23
10.4230/LIPIcs.FSTTCS.2021.24
article
Near-Optimal Cayley Expanders for Abelian Groups
Jalan, Akhil
1
Moshkovitz, Dana
1
Department of Computer Science, University of Texas at Austin, TX, USA
We give an efficient deterministic algorithm that outputs an expanding generating set for any finite abelian group. The size of the generating set is close to the randomized construction of Alon and Roichman [Alon and Roichman, 1994], improving upon various deterministic constructions in both the dependence on the dimension and the spectral gap. By obtaining optimal dependence on the dimension we resolve a conjecture of Azar, Motwani, and Naor [Azar et al., 1998] in the affirmative. Our technique is an extension of the bias amplification technique of Ta-Shma [Ta-Shma, 2017], who used random walks on expanders to obtain expanding generating sets over the additive group of 𝔽₂ⁿ. As a consequence, we obtain (i) randomness-efficient constructions of almost k-wise independent variables, (ii) a faster deterministic algorithm for the Remote Point Problem, (iii) randomness-efficient low-degree tests, and (iv) randomness-efficient verification of matrix multiplication.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.24/LIPIcs.FSTTCS.2021.24.pdf
Cayley graphs
Expander walks
Epsilon-biased sets
Derandomization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
25:1
25:19
10.4230/LIPIcs.FSTTCS.2021.25
article
Matchings, Critical Nodes, and Popular Solutions
Kavitha, Telikepalli
1
Tata Institute of Fundamental Research, Mumbai, India
We consider a matching problem in a marriage instance G. Every node has a strict preference order ranking its neighbors. There is a set C of prioritized or critical nodes and we are interested in only those matchings that match as many critical nodes as possible. Such matchings are useful in several applications and we call them critical matchings. A stable matching need not be critical. We consider a well-studied relaxation of stability called popularity. Our goal is to find a popular critical matching, i.e., a weak Condorcet winner within the set of critical matchings where nodes are voters. We show that popular critical matchings always exist in G and min-size/max-size such matchings can be efficiently computed.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.25/LIPIcs.FSTTCS.2021.25.pdf
Bipartite graphs
Stable matchings
LP-duality
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
26:1
26:17
10.4230/LIPIcs.FSTTCS.2021.26
article
Fast and Exact Convex Hull Simplification
Klimenko, Georgiy
1
Raichel, Benjamin
1
Department of Computer Science, University of Texas at Dallas, Richardson, TX, USA
Given a point set P in the plane, we seek a subset Q ⊆ P, whose convex hull gives a smaller and thus simpler representation of the convex hull of P. Specifically, let cost(Q,P) denote the Hausdorff distance between the convex hulls CH(Q) and CH(P). Then given a value ε > 0 we seek the smallest subset Q ⊆ P such that cost(Q,P) ≤ ε. We also consider the dual version, where given an integer k, we seek the subset Q ⊆ P which minimizes cost(Q,P), such that |Q| ≤ k. For these problems, when P is in convex position, we respectively give an O(n log²n) time algorithm and an O(n log³n) time algorithm, where the latter running time holds with high probability. When there is no restriction on P, we show the problem can be reduced to APSP in an unweighted directed graph, yielding an O(n^2.5302) time algorithm when minimizing k and an O(min{n^2.5302, kn^2.376}) time algorithm when minimizing ε, using prior results for APSP. Finally, we show our near linear algorithms for convex position give 2-approximations for the general case.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.26/LIPIcs.FSTTCS.2021.26.pdf
Convex hull
coreset
exact algorithm
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
27:1
27:23
10.4230/LIPIcs.FSTTCS.2021.27
article
Lower Bounds and Improved Algorithms for Asymmetric Streaming Edit Distance and Longest Common Subsequence
Li, Xin
1
Zheng, Yu
1
Department of Computer Science, Johns Hopkins University, Baltimore, MD, USA
In this paper, we study edit distance (ED) and longest common subsequence (LCS) in the asymmetric streaming model, introduced by Saks and Seshadhri [Saks and Seshadhri, 2013]. As an intermediate model between the random access model and the streaming model, this model allows one to have streaming access to one string and random access to the other string. Meanwhile, ED and LCS are both fundamental problems that are often studied on large strings, thus the (asymmetric) streaming model is ideal for studying these problems.
Our first main contribution is a systematic study of space lower bounds for ED and LCS in the asymmetric streaming model. Previously, there are no explicitly stated results in this context, although some lower bounds about LCS can be inferred from the lower bounds for longest increasing subsequence (LIS) in [Sun and Woodruff, 2007; Gál and Gopalan, 2010; Ergun and Jowhari, 2008]. Yet these bounds only work for large alphabet size. In this paper, we develop several new techniques to handle ED in general and LCS for small alphabet size, thus establishing strong lower bounds for both problems. In particular, our lower bound for ED provides an exponential separation between edit distance and Hamming distance in the asymmetric streaming model. Our lower bounds also extend to LIS and longest non-decreasing subsequence (LNS) in the standard streaming model. Together with previous results, our bounds provide an almost complete picture for these two problems.
As our second main contribution, we give improved algorithms for ED and LCS in the asymmetric streaming model. For ED, we improve the space complexity of the constant factor approximation algorithms in [Farhadi et al., 2020; Cheng et al., 2020] from Õ({n^δ}/δ) to O({d^δ}/δ polylog(n)), where n is the length of each string and d is the edit distance between the two strings. For LCS, we give the first 1/2+ε approximation algorithm with space n^δ for any constant δ > 0, over a binary alphabet. Our work leaves a plethora of intriguing open questions, including establishing lower bounds and designing algorithms for a natural generalization of LIS and LNS, which we call longest non-decreasing subsequence with threshold (LNST).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.27/LIPIcs.FSTTCS.2021.27.pdf
Asymmetric Streaming Model
Edit Distance
Longest Common Subsequence
Space Lower Bound
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
28:1
28:9
10.4230/LIPIcs.FSTTCS.2021.28
article
An ETH-Tight Algorithm for Multi-Team Formation
Lokshtanov, Daniel
1
Saurabh, Saket
2
3
Suri, Subhash
1
Xue, Jie
4
University of California, Santa Barbara, CA, USA
The Institute of Mathematical Sciences (HBNI), Chennai, India
University of Bergen, Norway
New York University Shanghai, China
In the Multi-Team Formation problem, we are given a ground set C of n candidates, each of which is characterized by a d-dimensional attribute vector in ℝ^d, and two positive integers α and β satisfying α β ≤ n. The goal is to form α disjoint teams T₁,...,T_α ⊆ C, each of which consists of β candidates in C, such that the total score of the teams is maximized, where the score of a team T is the sum of the h_j maximum values of the j-th attributes of the candidates in T, for all j ∈ {1,...,d}. Our main result is an 2^{2^O(d)} n^O(1)-time algorithm for Multi-Team Formation. This bound is ETH-tight since a 2^{2^{d/c}} n^O(1)-time algorithm for any constant c > 12 can be shown to violate the Exponential Time Hypothesis (ETH). Our algorithm runs in polynomial time for all dimensions up to d = clog log n for a sufficiently small constant c > 0. Prior to our work, the existence of a polynomial time algorithm was an open problem even for d = 3.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.28/LIPIcs.FSTTCS.2021.28.pdf
Team formation
Parameterized algorithms
Exponential Time Hypothesis
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
29:1
29:17
10.4230/LIPIcs.FSTTCS.2021.29
article
Dominating Set in Weakly Closed Graphs is Fixed Parameter Tractable
Lokshtanov, Daniel
1
Surianarayanan, Vaishali
1
University of California Santa Barbara, CA, USA
In the Dominating Set problem the input is a graph G and an integer k, the task is to determine whether there exists a vertex set S of size at most k so that every vertex not in S has at least one neighbor in S. We consider the parameterized complexity of the Dominating Set problem, parameterized by the solution size k, and the weak closure of the input graph G. Weak closure of graphs was recently introduced by Fox et al. [SIAM J. Comp. 2020 ] and captures sparseness and triadic closure properties found in real world graphs. A graph G is weakly c-closed if for every induced subgraph G' of G, there exists a vertex v ∈ V(G') such that every vertex u in V(G') which is non-adjacent to v has less than c common neighbors with v. The weak closure of G is the smallest integer γ such that G is weakly γ-closed. We give an algorithm for Dominating Set with running time k^O(γ² k³) n^O(1), resolving an open problem of Koana et al. [ISAAC 2020].
One of the ingredients of our algorithm is a proof that the VC-dimension of (the set system defined by the closed neighborhoods of the vertices of) a weakly γ-closed graph is upper bounded by 6γ. This result may find further applications in the study of weakly closed graphs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.29/LIPIcs.FSTTCS.2021.29.pdf
Dominating Set
Weakly Closed Graphs
FPT
Domination Cores
VC-dimension
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
30:1
30:21
10.4230/LIPIcs.FSTTCS.2021.30
article
Popular Matchings in the Hospital-Residents Problem with Two-Sided Lower Quotas
Nasre, Meghana
1
Nimbhorkar, Prajakta
2
3
Ranjan, Keshav
1
Sarkar, Ankita
4
IIT Madras, Chennai, India
Chennai Mathematical Institute, India
UMI ReLaX, Chennai, India
Dartmouth College, Hanover, NH, USA
We consider the hospital-residents problem where both hospitals and residents can have lower quotas. The input is a bipartite graph G = (ℛ∪ℋ,E), each vertex in ℛ∪ℋ has a strict preference ordering over its neighbors. The sets ℛ and ℋ denote the sets of residents and hospitals respectively. Each hospital has an upper and a lower quota denoting the maximum and minimum number of residents that can be assigned to it. Residents have upper quota equal to one, however, there may be a requirement that some residents must not be left unassigned in the output matching. We call this as the residents' lower quota.
We show that whenever the set of matchings satisfying all the lower and upper quotas is non-empty, there always exists a matching that is popular among the matchings in this set. We give a polynomial-time algorithm to compute such a matching.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.30/LIPIcs.FSTTCS.2021.30.pdf
Matching
Popularity
Lower quota
Preferences
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
31:1
31:8
10.4230/LIPIcs.FSTTCS.2021.31
article
Property B: Two-Coloring Non-Uniform Hypergraphs
Radhakrishnan, Jaikumar
1
Srinivasan, Aravind
2
School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, India
Department of Computer Science and UMIACS, University of Maryland at College Park, MD, USA
The following is a classical question of Erdős (Nordisk Matematisk Tidskrift, 1963) and of Erdős and Lovász (Colloquia Mathematica Societatis János Bolyai, vol. 10, 1975). Given a hypergraph ℱ with minimum edge-size k, what is the largest function g(k) such that if the expected number of monochromatic edges in ℱ is at most g(k) when the vertices of ℱ are colored red and blue randomly and independently, then we are guaranteed that ℱ is two-colorable? Duraj, Gutowski and Kozik (ICALP 2018) have shown that g(k) ≥ Ω(log k). On the other hand, if ℱ is k-uniform, the lower bound on g(k) is much higher: g(k) ≥ Ω(√{k / log k}) (Radhakrishnan and Srinivasan, Rand. Struct. Alg., 2000). In order to bridge this gap, we define a family of locally-almost-uniform hypergraphs, for which we show, via the randomized algorithm of Cherkashin and Kozik (Rand. Struct. Alg., 2015), that g(k) can be much higher than Ω(log k), e.g., 2^Ω(√{log k}) under suitable conditions.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.31/LIPIcs.FSTTCS.2021.31.pdf
Hypergraph coloring
Propery B
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
32:1
32:22
10.4230/LIPIcs.FSTTCS.2021.32
article
Harmonic Algorithms for Packing d-Dimensional Cuboids into Bins
Sharma, Eklavya
1
Department of Computer Science and Automation, Indian Institute of Science, Bengaluru, India
We explore approximation algorithms for the d-dimensional geometric bin packing problem (dBP). Caprara [Caprara, 2008] gave a harmonic-based algorithm for dBP having an asymptotic approximation ratio (AAR) of (T_∞)^{d-1} (where T_∞ ≈ 1.691). However, their algorithm doesn't allow items to be rotated. This is in contrast to some common applications of dBP, like packing boxes into shipping containers. We give approximation algorithms for dBP when items can be orthogonally rotated about all or a subset of axes. We first give a fast and simple harmonic-based algorithm having AAR T_∞^d. We next give a more sophisticated harmonic-based algorithm, which we call HGaP_k, having AAR (T_∞)^{d-1}(1+ε). This gives an AAR of roughly 2.860 + ε for 3BP with rotations, which improves upon the best-known AAR of 4.5. In addition, we study the multiple-choice bin packing problem that generalizes the rotational case. Here we are given n sets of d-dimensional cuboidal items and we have to choose exactly one item from each set and then pack the chosen items. Our algorithms also work for the multiple-choice bin packing problem. We also give fast and simple approximation algorithms for the multiple-choice versions of dD strip packing and dD geometric knapsack.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.32/LIPIcs.FSTTCS.2021.32.pdf
Geometric bin packing
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
33:1
33:22
10.4230/LIPIcs.FSTTCS.2021.33
article
Resilience of Timed Systems
Akshay, S.
1
https://orcid.org/0000-0002-2471-5997
Genest, Blaise
2
https://orcid.org/0000-0002-5758-1876
Hélouët, Loïc
3
https://orcid.org/0000-0001-7056-2672
Krishna, S.
1
https://orcid.org/0000-0003-0925-398X
Roychowdhury, Sparsa
1
https://orcid.org/0000-0003-3583-7612
IIT Bombay, Mumbai, India
Univ. Rennes, CNRS, IRISA, Rennes, France
Univ. Rennes, INRIA, IRISA, Rennes, France
This paper addresses reliability of timed systems in the setting of resilience, that considers the behaviors of a system when unspecified timing errors such as missed deadlines occur. Given a fault model that allows transitions to fire later than allowed by their guard, a system is universally resilient (or self-resilient) if after a fault, it always returns to a timed behavior of the non-faulty system. It is existentially resilient if after a fault, there exists a way to return to a timed behavior of the non-faulty system, that is, if there exists a controller which can guide the system back to a normal behavior. We show that universal resilience of timed automata is undecidable, while existential resilience is decidable, in EXPSPACE. To obtain better complexity bounds and decidability of universal resilience, we consider untimed resilience, as well as subclasses of timed automata.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.33/LIPIcs.FSTTCS.2021.33.pdf
Timed automata
Fault tolerance
Integer-resets
Resilience
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
34:1
34:15
10.4230/LIPIcs.FSTTCS.2021.34
article
On the Complexity of Intersection Non-emptiness for Star-Free Language Classes
Arrighi, Emmanuel
1
https://orcid.org/0000-0002-0326-1893
Fernau, Henning
2
https://orcid.org/0000-0002-4444-3220
Hoffmann, Stefan
2
https://orcid.org/0000-0002-7866-075X
Holzer, Markus
3
https://orcid.org/0000-0003-4224-4014
Jecker, Ismaël
4
https://orcid.org/0000-0002-6527-4470
de Oliveira Oliveira, Mateus
1
https://orcid.org/0000-0001-7798-7446
Wolf, Petra
2
https://orcid.org/0000-0003-3097-3906
University of Bergen, Norway
Fachbereich IV, Informatikwissenschaften, Universität Trier, Germany
Institut für Informatik, Universität Giessen, Germany
Institute of Science and Technology, Klosterneuburg, Austria
In the Intersection Non-emptiness problem, we are given a list of finite automata A_1, A_2,… , A_m over a common alphabet Σ as input, and the goal is to determine whether some string w ∈ Σ^* lies in the intersection of the languages accepted by the automata in the list. We analyze the complexity of the Intersection Non-emptiness problem under the promise that all input automata accept a language in some level of the dot-depth hierarchy, or some level of the Straubing-Thérien hierarchy. Automata accepting languages from the lowest levels of these hierarchies arise naturally in the context of model checking. We identify a dichotomy in the dot-depth hierarchy by showing that the problem is already NP-complete when all input automata accept languages of the levels B_0 or B_{1/2} and already PSPACE-hard when all automata accept a language from the level B_1. Conversely, we identify a tetrachotomy in the Straubing-Thérien hierarchy. More precisely, we show that the problem is in AC^0 when restricted to level L_0; complete for L or NL, depending on the input representation, when restricted to languages in the level L_{1/2}; NP-complete when the input is given as DFAs accepting a language in L_1 or L_{3/2}; and finally, PSPACE-complete when the input automata accept languages in level L_2 or higher. Moreover, we show that the proof technique used to show containment in NP for DFAs accepting languages in L_1 or L_{3/2} does not generalize to the context of NFAs. To prove this, we identify a family of languages that provide an exponential separation between the state complexity of general NFAs and that of partially ordered NFAs. To the best of our knowledge, this is the first superpolynomial separation between these two models of computation.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.34/LIPIcs.FSTTCS.2021.34.pdf
Intersection Non-emptiness Problem
Star-Free Languages
Straubing-Thérien Hierarchy
dot-depth Hierarchy
Commutative Languages
Complexity
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
35:1
35:16
10.4230/LIPIcs.FSTTCS.2021.35
article
Complexity of Coverability in Bounded Path Broadcast Networks
Balasubramanian, A. R.
1
https://orcid.org/0000-0002-7258-5445
Technische Universität München, Germany
Broadcast networks are a formalism of distributed computation that allow one to model networks of identical nodes communicating through message broadcasts over a communication topology that does not change over the course of executions. The parameterized verification problem for these networks amounts to proving correctness of a property for any number of nodes, and on all executions. Dually speaking, this problem asks for the existence of an execution of the broadcast network that violates a given property. One specific instance of parameterized verification is the coverability problem which asks whether there is an execution of the network in which some node reaches a given state of the broadcast protocol. This problem was proven to be undecidable by Delzanno, Sangnier and Zavattaro (CONCUR 2010). In the same paper, the authors also prove that, if we additionally assume that the underlying communication topology has a bound on the longest path, then the coverability problem becomes decidable.
In this paper, we provide complexity results for the above problem and prove that the coverability problem for bounded-path topologies is 𝐅_ε₀-complete, where 𝐅_ε₀ is a class in the fast-growing hierarchy of complexity classes. This solves an open problem of Hasse, Schmitz and Schnoebelen (LMCS, Vol 10, Issue 4).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.35/LIPIcs.FSTTCS.2021.35.pdf
Parameterized verification
Bounded path networks
Fast-growing complexity classes
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
36:1
36:15
10.4230/LIPIcs.FSTTCS.2021.36
article
On Classical Decidable Logics Extended with Percentage Quantifiers and Arithmetics
Bednarczyk, Bartosz
1
2
https://orcid.org/0000-0002-8267-7554
Orłowska, Maja
2
Pacanowska, Anna
2
Tan, Tony
3
Computational Logic Group, Technische Universität Dresden, Germany
Institute of Computer Science, University of Wrocław, Poland
Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan
During the last decades, a lot of effort was put into identifying decidable fragments of first-order logic. Such efforts gave birth, among the others, to the two-variable fragment and the guarded fragment, depending on the type of restriction imposed on formulae from the language. Despite the success of the mentioned logics in areas like formal verification and knowledge representation, such first-order fragments are too weak to express even the simplest statistical constraints, required for modelling of influence networks or in statistical reasoning.
In this work we investigate the extensions of these classical decidable logics with percentage quantifiers, specifying how frequently a formula is satisfied in the indented model. We show, surprisingly, that all the mentioned decidable fragments become undecidable under such extension, sharpening the existing results in the literature. Our negative results are supplemented by decidability of the two-variable guarded fragment with even more expressive counting, namely Presburger constraints. Our results can be applied to infer decidability of various modal and description logics, e.g. Presburger Modal Logics with Converse or ALCI, with expressive cardinality constraints.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.36/LIPIcs.FSTTCS.2021.36.pdf
statistical reasoning
knowledge representation
satisfiability
fragments of first-order logic
guarded fragment
two-variable fragment
(un)decidability
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
37:1
37:13
10.4230/LIPIcs.FSTTCS.2021.37
article
Branching Automata and Pomset Automata
Bedon, Nicolas
1
LITIS (EA 4108), University of Rouen, France
We compare, in terms of expressive power, two notions of automata recognizing finite N-free pomsets: branching automata by Lodaya and Weil [Lodaya and Weil, 1998; Lodaya and Weil, 1998; Lodaya and Weil, 2000; Lodaya and Weil, 2001] and pomset automata by Kappé, Brunet, Luttik, Silva and Zanasi [Kappé et al., 2018]. In the general case, they are equivalent. We also consider sub-classes of both kind of automata that we prove equivalent.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.37/LIPIcs.FSTTCS.2021.37.pdf
Finite N-free Pomsets
Finite Series-Parallel Pomsets
Branching Automata
Pomset Automata
Series-Parallel Rational Languages
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
38:1
38:20
10.4230/LIPIcs.FSTTCS.2021.38
article
History Determinism vs. Good for Gameness in Quantitative Automata
Boker, Udi
1
Lehtinen, Karoliina
2
https://orcid.org/0000-0003-1171-8790
Reichman University, Herzliya, Israel
CNRS, Marseille-Aix Université, Université de Toulon, LIS, Marseille, France
Automata models between determinism and nondeterminism/alternations can retain some of the algorithmic properties of deterministic automata while enjoying some of the expressiveness and succinctness of nondeterminism. We study three closely related such models - history determinism, good for gameness and determinisability by pruning - on quantitative automata.
While in the Boolean setting, history determinism and good for gameness coincide, we show that this is no longer the case in the quantitative setting: good for gameness is broader than history determinism, and coincides with a relaxed version of it, defined with respect to thresholds. We further identify criteria in which history determinism, which is generally broader than determinisability by pruning, coincides with it, which we then apply to typical quantitative automata types.
As a key application of good for games and history deterministic automata is synthesis, we clarify the relationship between the two notions and various quantitative synthesis problems. We show that good-for-games automata are central for "global" (classical) synthesis, while "local" (good-enough) synthesis reduces to deciding whether a nondeterministic automaton is history deterministic.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.38/LIPIcs.FSTTCS.2021.38.pdf
Good for games
history determinism
alternation
quantitative automata
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
39:1
39:15
10.4230/LIPIcs.FSTTCS.2021.39
article
Local First-Order Logic with Two Data Values
Bollig, Benedikt
1
Sangnier, Arnaud
2
Stietel, Olivier
2
1
Université Paris-Saclay, CNRS, ENS Paris-Saclay, LMF, France
IRIF, Université de Paris, CNRS, France
We study first-order logic over unordered structures whose elements carry two data values from an infinite domain. Data values can be compared wrt. equality so that the formalism is suitable to specify the input-output behavior of various distributed algorithms. As the logic is undecidable in general, we introduce a family of local fragments that restrict quantification to neighborhoods of a given reference point. Our main result establishes decidability of the satisfiability problem for one of these non-trivial local fragments. On the other hand, already slightly more general local logics turn out to be undecidable. Altogether, we draw a landscape of formalisms that are suitable for the specification of systems with data and open up new avenues for future research.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.39/LIPIcs.FSTTCS.2021.39.pdf
first-order logic
data values
specification of distributed algorithms
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
40:1
40:18
10.4230/LIPIcs.FSTTCS.2021.40
article
Diagrammatic Polyhedral Algebra
Bonchi, Filippo
1
https://orcid.org/0000-0002-3433-723X
Di Giorgio, Alessandro
1
https://orcid.org/0000-0002-6428-6461
Sobociński, Paweł
2
https://orcid.org/0000-0002-7992-9685
University of Pisa, Italy
Tallinn University of Technology, Estonia
We extend the theory of Interacting Hopf algebras with an order primitive, and give a sound and complete axiomatisation of the prop of polyhedral cones. Next, we axiomatise an affine extension and prove soundness and completeness for the prop of polyhedra.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.40/LIPIcs.FSTTCS.2021.40.pdf
String diagrams
Polyhedral cones
Polyhedra
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
41:1
41:14
10.4230/LIPIcs.FSTTCS.2021.41
article
From Local to Global Determinacy in Concurrent Graph Games
Bordais, Benjamin
1
Bouyer, Patricia
1
Le Roux, Stéphane
1
Université Paris-Saclay, CNRS, ENS Paris-Saclay, LMF, 91190 Gif-sur-Yvette, France
In general, finite concurrent two-player reachability games are only determined in a weak sense: the supremum probability to win can be approached via stochastic strategies, but cannot be realized.
We introduce a class of concurrent games that are determined in a much stronger sense, and in a way, it is the largest class with this property. To this end, we introduce the notion of local interaction at a state of a graph game: it is a game form whose outcomes (i.e. a table whose entries) are the next states, which depend on the concurrent actions of the players. By definition, a game form is determined iff it always yields games that are determined via deterministic strategies when used as a local interaction in a Nature-free, one-shot reachability game. We show that if all the local interactions of a graph game with Borel objective are determined game forms, the game itself is determined: if Nature does not play, one player has a winning strategy; if Nature plays, both players have deterministic strategies that maximize the probability to win. This constitutes a clear-cut separation: either a game form behaves poorly already when used alone with basic objectives, or it behaves well even when used together with other well-behaved game forms and complex objectives.
Existing results for positional and finite-memory determinacy in turn-based games are extended this way to concurrent games with determined local interactions (CG-DLI).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.41/LIPIcs.FSTTCS.2021.41.pdf
Concurrent games
Game forms
Local interaction
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
42:1
42:23
10.4230/LIPIcs.FSTTCS.2021.42
article
Quantitative Verification on Product Graphs of Small Treewidth
Chatterjee, Krishnendu
1
Ibsen-Jensen, Rasmus
2
Pavlogiannis, Andreas
3
https://orcid.org/0000-0002-8943-0722
IST Austria, Klosterneuburg, Austria
University of Liverpool, UK
Aarhus University, Denmark
Product graphs arise naturally in formal verification and program analysis. For example, the analysis of two concurrent threads requires the product of two component control-flow graphs, and for language inclusion of deterministic automata the product of two automata is constructed. In many cases, the component graphs have constant treewidth, e.g., when the input contains control-flow graphs of programs. We consider the algorithmic analysis of products of two constant-treewidth graphs with respect to three classic specification languages, namely, (a) algebraic properties, (b) mean-payoff properties, and (c) initial credit for energy properties.
Our main contributions are as follows. Consider a graph G that is the product of two constant-treewidth graphs of size n each. First, given an idempotent semiring, we present an algorithm that computes the semiring transitive closure of G in time Õ(n⁴). Since the output has size Θ(n⁴), our algorithm is optimal (up to polylog factors). Second, given a mean-payoff objective, we present an O(n³)-time algorithm for deciding whether the value of a starting state is non-negative, improving the previously known O(n⁴) bound. Third, given an initial credit for energy objective, we present an O(n⁵)-time algorithm for computing the minimum initial credit for all nodes of G, improving the previously known O(n⁸) bound. At the heart of our approach lies an algorithm for the efficient construction of strongly-balanced tree decompositions of constant-treewidth graphs. Given a constant-treewidth graph G' of n nodes and a positive integer λ, our algorithm constructs a binary tree decomposition of G' of width O(λ) with the property that the size of each subtree decreases geometrically with rate (1/2 + 2^{-λ}).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.42/LIPIcs.FSTTCS.2021.42.pdf
graph algorithms
algebraic paths
mean-payoff
initial credit for energy
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
43:1
43:16
10.4230/LIPIcs.FSTTCS.2021.43
article
Synthesizing Computable Functions from Rational Specifications over Infinite Words
Filiot, Emmanuel
1
https://orcid.org/0000-0002-2520-5630
Winter, Sarah
1
https://orcid.org/0000-0002-3499-1995
Université libre de Bruxelles, Brussels, Belgium
The synthesis problem asks to automatically generate, if it exists, an algorithm from a specification of correct input-output pairs. In this paper, we consider the synthesis of computable functions of infinite words, for a classical Turing computability notion over infinite inputs. We consider specifications which are rational relations of infinite words, i.e., specifications defined by non-deterministic parity transducers. We prove that the synthesis problem of computable functions from rational specifications is undecidable. We provide an incomplete but sound reduction to some parity game, such that if Eve wins the game, then the rational specification is realizable by a computable function. We prove that this function is even computable by a deterministic two-way transducer.
We provide a sufficient condition under which the latter game reduction is complete. This entails the decidability of the synthesis problem of computable functions, which we proved to be ExpTime-complete, for a large subclass of rational specifications, namely deterministic rational specifications. This subclass contains the class of automatic relations over infinite words, a yardstick in reactive synthesis.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.43/LIPIcs.FSTTCS.2021.43.pdf
uniformization
synthesis
transducers
continuity
computability
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
44:1
44:18
10.4230/LIPIcs.FSTTCS.2021.44
article
Confluence of Conditional Rewriting in Logic Form
Gutiérrez, Raúl
1
https://orcid.org/0000-0002-3984-2868
Lucas, Salvador
2
https://orcid.org/0000-0001-9923-2108
Vítores, Miguel
3
Universidad Politécnica de Madrid, Spain
DSIC & VRAIN, Universitat Politècnica de València, Spain
VRAIN, Universitat Politècnica de València, Spain
We characterize conditional rewriting as satisfiability in a Herbrand-like model of terms where variables are also included as fresh constant symbols extending the original signature. Confluence of conditional rewriting and joinability of conditional critical pairs is characterized similarly. Joinability of critical pairs is then translated into combinations of (in)feasibility problems which can be efficiently handled by a number of automatic tools. This permits a more efficient use of standard results for proving confluence of conditional term rewriting systems, most of them relying on auxiliary proofs of joinability of conditional critical pairs, perhaps with additional syntactical and (operational) termination requirements on the system. Our approach has been implemented in a new system: CONFident . Its ability to (dis)prove confluence of conditional term rewriting systems is witnessed by means of some benchmarks comparing our tool with existing tools for similar purposes.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.44/LIPIcs.FSTTCS.2021.44.pdf
Confluence
Program analysis
Rewriting-based systems
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
45:1
45:21
10.4230/LIPIcs.FSTTCS.2021.45
article
On the Expressive Equivalence of TPTL in the Pointwise and Continuous Semantics
Holla, Raveendra
1
Deka, Nabarun
2
D'Souza, Deepak
2
Citrix Systems India Pvt. Ltd., Bangalore, India
Indian Institute of Science Bangalore, India
We consider a first-order logic with linear constraints interpreted in a pointwise and continuous manner over timed words. We show that the two interpretations of this logic coincide in terms of expressiveness, via an effective transformation of sentences from one logic to the other. As a consequence it follows that the pointwise and continuous semantics of the logic TPTL with the since operator also coincide. Along the way we exhibit a useful normal form for sentences in these logics.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.45/LIPIcs.FSTTCS.2021.45.pdf
Real-Time Logics
First-Order Logics
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
46:1
46:13
10.4230/LIPIcs.FSTTCS.2021.46
article
Separating Regular Languages over Infinite Words with Respect to the Wagner Hierarchy
Hugenroth, Christopher
1
TU Ilmenau, Germany
We investigate the separation problem for regular ω-languages with respect to the Wagner hierarchy where the input languages are given as deterministic Muller automata (DMA). We show that a minimal separating DMA can be computed in exponential time and that some languages require separators of exponential size. Further, we show that in this setting it can be decided in polynomial time whether a separator exists on a certain level of the Wagner hierarchy and that emptiness of the intersection of two languages given by DMAs can be decided in polynomial time. Finally, we show that separation can also be decided in polynomial time if the input languages are given as deterministic parity automata.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.46/LIPIcs.FSTTCS.2021.46.pdf
Separation
Regular
Wagner Hierarchy
Muller Automata
Parity Automata
Product Automata
Membership
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
47:1
47:16
10.4230/LIPIcs.FSTTCS.2021.47
article
Normal Sequences with Non-Maximal Automatic Complexity
Jordon, Liam
1
https://orcid.org/0000-0003-0583-666X
Moser, Philippe
1
Department of Computer Science, Maynooth University, Maynooth, Ireland
This paper examines Automatic Complexity, a complexity notion introduced by Shallit and Wang in 2001 [Jeffrey O. Shallit and Ming-wei Wang, 2001]. We demonstrate that there exists a normal sequence T such that I(T) = 0 and S(T) ≤ 1/2, where I(T) and S(T) are the lower and upper automatic complexity rates of T respectively. We furthermore show that there exists a Champernowne sequence C, i.e. a sequence formed by concatenating all strings of length one followed by concatenating all strings of length two and so on, such that S(C) ≤ 2/3.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.47/LIPIcs.FSTTCS.2021.47.pdf
Automatic Complexity
finite-state complexity
normal sequences
Champernowne sequences
de Bruijn strings
Kolmogorov complexity
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
48:1
48:16
10.4230/LIPIcs.FSTTCS.2021.48
article
Approximate Bisimulation Minimisation
Kiefer, Stefan
1
https://orcid.org/0000-0003-4173-6877
Tang, Qiyi
1
https://orcid.org/0000-0002-9265-3011
Department of Computer Science, University of Oxford, UK
We propose polynomial-time algorithms to minimise labelled Markov chains whose transition probabilities are not known exactly, have been perturbed, or can only be obtained by sampling. Our algorithms are based on a new notion of an approximate bisimulation quotient, obtained by lumping together states that are exactly bisimilar in a slightly perturbed system. We present experiments that show that our algorithms are able to recover the structure of the bisimulation quotient of the unperturbed system.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.48/LIPIcs.FSTTCS.2021.48.pdf
Markov chains
Behavioural metrics
Bisimulation
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
49:1
49:15
10.4230/LIPIcs.FSTTCS.2021.49
article
Simple Derivation Systems for Proving Sufficient Completeness of Non-Terminating Term Rewriting Systems
Kikuchi, Kentaro
1
Aoto, Takahito
2
Tohoku University, Sendai, Japan
Niigata University, Niigata, Japan
A term rewriting system (TRS) is said to be sufficiently complete when each function yields some value for any input. Proof methods for sufficient completeness of terminating TRSs have been well studied. In this paper, we introduce a simple derivation system for proving sufficient completeness of possibly non-terminating TRSs. The derivation system consists of rules to manipulate a set of guarded terms, and sufficient completeness of a TRS holds if there exists a successful derivation for each function symbol. We also show that variations of the derivation system are useful for proving special cases of local sufficient completeness of TRSs, which is a generalised notion of sufficient completeness.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.49/LIPIcs.FSTTCS.2021.49.pdf
Term rewriting
Sufficient completeness
Local sufficient completeness
Non-termination
Derivation rule
Well-founded induction schema
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
50:1
50:14
10.4230/LIPIcs.FSTTCS.2021.50
article
Parikh Images of Register Automata
Lasota, Sławomir
1
https://orcid.org/0000-0001-8674-4470
Pattathurajan, Mohnish
1
University of Warsaw, Poland
As it has been recently shown, Parikh images of languages of nondeterministic one-register automata are rational (but not semilinear in general), but it is still open if the property extends to all register automata. We identify a subclass of nondeterministic register automata, called hierarchical register automata (HRA), with the following two properties: every rational language is recognised by a HRA; and Parikh image of the language of every HRA is rational. In consequence, these two properties make HRA an automata-theoretic characterisation of languages of nondeterministic register automata with rational Parikh images.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.50/LIPIcs.FSTTCS.2021.50.pdf
Sets with atoms
register automata
Parikh images
rational sets
hierarchical register automata
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
51:1
51:20
10.4230/LIPIcs.FSTTCS.2021.51
article
Concrete Categorical Model of a Quantum Circuit Description Language with Measurement
Lee, Dongho
1
Perrelle, Valentin
2
Valiron, Benoît
3
Xu, Zhaowei
4
Université Paris-Saclay, CentraleSupélec, LMF, France & CEA, List, France
Université Paris-Saclay, CEA, List, France
Université Paris-Saclay, CentraleSupélec, LMF, France
Université Paris-Saclay, LMF, France
In this paper, we introduce dynamic lifting to a quantum circuit-description language, following the Proto-Quipper language approach. Dynamic lifting allows programs to transfer the result of measuring quantum data - qubits - into classical data - booleans -. We propose a type system and an operational semantics for the language and we state safety properties. Next, we introduce a concrete categorical semantics for the proposed language, basing our approach on a recent model from Rios&Selinger for Proto-Quipper-M. Our approach is to construct on top of a concrete category of circuits with measurements a Kleisli category, capturing as a side effect the action of retrieving classical content out of a quantum memory. We then show a soundness result for this semantics.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.51/LIPIcs.FSTTCS.2021.51.pdf
Categorical semantics
Operational semantics
Quantum circuit description language
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
213
52:1
52:17
10.4230/LIPIcs.FSTTCS.2021.52
article
Linear-Time Temporal Logic with Team Semantics: Expressivity and Complexity
Virtema, Jonni
1
2
https://orcid.org/0000-0002-1582-3718
Hofmann, Jana
3
https://orcid.org/0000-0003-1660-2949
Finkbeiner, Bernd
3
https://orcid.org/0000-0002-4280-8441
Kontinen, Juha
4
https://orcid.org/0000-0003-0115-5154
Yang, Fan
4
https://orcid.org/0000-0003-0392-6522
Institute for Theoretical Computer Science, Leibniz Universität Hannover, Germany
Department of Computer Science, University of Sheffield, UK
CISPA Helmholtz Center for Information Security, Saarbrücken, Germany
Department of Mathematics and Statistics, University of Helsinki, Finland
We study the expressivity and complexity of model checking of linear temporal logic with team semantics (TeamLTL). TeamLTL, despite being a purely modal logic, is capable of defining hyperproperties, i.e., properties which relate multiple execution traces. TeamLTL has been introduced quite recently and only few results are known regarding its expressivity and its model checking problem. We relate the expressivity of TeamLTL to logics for hyperproperties obtained by extending LTL with trace and propositional quantifiers (HyperLTL and HyperQPTL). By doing so, we obtain a number of model checking results for TeamLTL and identify its undecidability frontier. In particular, we show decidability of model checking of the so-called left-flat fragment of any downward closed TeamLTL -extension. Moreover, we establish that the model checking problem of TeamLTL with Boolean disjunction and inclusion atoms is undecidable.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.52/LIPIcs.FSTTCS.2021.52.pdf
Linear temporal logic
Hyperproperties
Model Checking
Expressivity