123 Search Results for "Potapov, Igor"

Volume

LIPIcs, Volume 117

43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

MFCS 2018, August 27-31, 2018, Liverpool, GB

Editors: Igor Potapov, Paul Spirakis, and James Worrell

Document
DOI: 10.4230/LIPIcs.STACS.2026.24
Foremost, Fastest, Shortest: Temporal Graph Realization Under Various Path Metrics

Authors: Justine Cauvi, Nils Morawietz, and Laurent Viennot

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
In this work, we follow the current trend on temporal graph realization, where one is given a property P and the goal is to determine whether there is a temporal graph, that is, a graph where the edge set changes over time, with property P. We consider the problems where the given property P is a prescribed matrix for the duration, length, or earliest arrival time of pairwise temporal paths. This means that we are given a matrix D and ask whether there is a temporal graph such that for any ordered pair of vertices (s,t), D_{s,t} equals the duration (length, or earliest arrival time, respectively) of any temporal path from s to t minimizing that specific temporal path metric. For shortest and earliest arrival temporal paths, we are the first to consider these problems as far as we know. We analyze these problems for many settings such as: strict and non-strict paths, periodic and non-periodic temporal graphs, and limited number of labels per edge (limited number of occurrences per edge over time). In contrast to all other path metrics, we show that for the earliest arrival times, we can achieve polynomial-time algorithms in periodic and non-periodic temporal graphs and for strict and and non-strict paths. However, the problem becomes NP-hard when the matrix does not contain a single integer but a set or range of possible allowed values. As we show, the problem can still be solved efficiently in this scenario, when the number of entries with more than one value is small, that is, we develop an FPT-algorithm for the number of such entries. For the setting of fastest paths, we achieve new hardness results that answers an open question by Klobas, Mertzios, Molter, and Spirakis [Theor. Comput. Sci. '25] about the parameterized complexity of the problem with respect to the vertex cover number and significantly improves over a previous hardness result for the feedback vertex set number. When considering shortest paths, we show that the periodic versions are polynomial-time solvable whereas the non-periodic versions become NP-hard.
Cite as

Justine Cauvi, Nils Morawietz, and Laurent Viennot. Foremost, Fastest, Shortest: Temporal Graph Realization Under Various Path Metrics. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cauvi_et_al:LIPIcs.STACS.2026.24,
  author =	{Cauvi, Justine and Morawietz, Nils and Viennot, Laurent},
  title =	{{Foremost, Fastest, Shortest: Temporal Graph Realization Under Various Path Metrics}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.24},
  URN =		{urn:nbn:de:0030-drops-255139},
  doi =		{10.4230/LIPIcs.STACS.2026.24},
  annote =	{Keywords: network design, temporal paths, foremost paths, fastest paths, shortest paths, non-strict paths, periodic temporal graphs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.64
One-Clock Synthesis Problems

Authors: Sławomir Lasota, Mathieu Lehaut, Julie Parreaux, and Radosław Piórkowski

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We study a generalisation of Büchi-Landweber games to the timed setting. The winning condition is specified by a non-deterministic timed automaton, and one of the players can elapse time. We perform a systematic study of synthesis problems in all variants of timed games, depending on which player’s winning condition is specified, and which player’s strategy (or controller, a finite-memory strategy) is sought. As our main result we prove ubiquitous undecidability in all the variants, both for strategy and controller synthesis, already for winning conditions specified by one-clock automata. This strengthens and generalises previously known undecidability results. We also fully characterise those cases where finite memory is sufficient to win, namely existence of a strategy implies existence of a controller. All our results are stated in the timed setting, while analogous results hold in the data setting where one-clock automata are replaced by one-register ones.
Cite as

Sławomir Lasota, Mathieu Lehaut, Julie Parreaux, and Radosław Piórkowski. One-Clock Synthesis Problems. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 64:1-64:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lasota_et_al:LIPIcs.STACS.2026.64,
  author =	{Lasota, S{\l}awomir and Lehaut, Mathieu and Parreaux, Julie and Pi\'{o}rkowski, Rados{\l}aw},
  title =	{{One-Clock Synthesis Problems}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{64:1--64:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.64},
  URN =		{urn:nbn:de:0030-drops-255533},
  doi =		{10.4230/LIPIcs.STACS.2026.64},
  annote =	{Keywords: timed automata, register automata, B\"{u}chi-Landweber games, Church synthesis problem, reactive synthesis problem}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.60
The Asymptotic Size of Finite Irreducible Semigroups of Rational Matrices

Authors: Stefan Kiefer and Andrew Ryzhikov

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We study finite semigroups of n × n matrices with rational entries. Such semigroups provide a rich generalization of transition monoids of unambiguous (and, in particular, deterministic) finite automata. In this paper we determine the maximum size of finite semigroups of rational n × n matrices, with the goal of shedding more light on the structure of such matrix semigroups. While in general such semigroups can be arbitrarily large in terms of n, a classical result of Schützenberger from 1962 implies an upper bound of 2^{𝒪(n² log n)} for irreducible semigroups, i.e., the only subspaces of ℚⁿ that are invariant for all matrices in the semigroup are ℚⁿ and the subspace consisting only of the zero vector. Irreducible matrix semigroups can be viewed as the building blocks of general matrix semigroups, and as such play an important role in mathematics and computer science. From the point of view of automata theory, they generalize strongly connected automata. Using a very different technique from that of Schützenberger, we improve the upper bound on the cardinality to 3^{n²}. This is the main result of the paper. The bound is in some sense tight, as we show that there exists, for every n, a finite irreducible semigroup with 3^{⌊ n²/4 ⌋} rational matrices. Our main result also leads to an improvement of a bound, due to Almeida and Steinberg, on the mortality threshold. The mortality threshold is a number 𝓁 such that if the zero matrix is in the semigroup, then the zero matrix can be written as a product of at most 𝓁 matrices from any subset that generates the semigroup.
Cite as

Stefan Kiefer and Andrew Ryzhikov. The Asymptotic Size of Finite Irreducible Semigroups of Rational Matrices. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 60:1-60:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kiefer_et_al:LIPIcs.STACS.2026.60,
  author =	{Kiefer, Stefan and Ryzhikov, Andrew},
  title =	{{The Asymptotic Size of Finite Irreducible Semigroups of Rational Matrices}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{60:1--60:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.60},
  URN =		{urn:nbn:de:0030-drops-255496},
  doi =		{10.4230/LIPIcs.STACS.2026.60},
  annote =	{Keywords: finite matrix semigroups, irreducible matrix semigroups, matrix mortality, aperiodic semigroups, unambiguous automata, transition monoids}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.8
Parameterized Algorithms for the Drone Delivery Problem

Authors: Simon Bartlmae, Andreas Hene, Joshua Könen, and Heiko Röglin

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Timely delivery and optimal routing remain fundamental challenges in the modern logistics industry. Building on prior work that considers single-package delivery across networks using multiple types of collaborative agents with restricted movement areas (e.g., drones or trucks), we examine the complexity of the problem under structural and operational constraints. Our focus is on minimizing total delivery time by coordinating agents that differ in speed and movement range across a graph. This problem formulation aligns with the recently proposed Drone Delivery Problem with respect to delivery time (DDT), introduced by Erlebach et al. [ISAAC 2022]. We first resolve an open question posed by Erlebach et al. [ISAAC 2022] by showing that even when the delivery network is a path graph, DDT admits no polynomial-time approximation within any polynomially encodable factor a(n), unless P=NP. Additionally, we identify the intersection graph of the agents, where nodes represent agents and edges indicate an overlap of the movement areas of two agents, as an important structural concept. For path graphs, we show that DDT becomes tractable when parameterized by the treewidth w of the intersection graph, and we present an exact FPT algorithm with running time f(w)⋅poly(n,k), for some computable function f. For general graphs, we give an FPT algorithm with running time f(Δ,w)⋅poly(n,k), where Δ is the maximum degree of the intersection graph. In the special case where the intersection graph is a tree, we provide a simple polynomial-time algorithm.
Cite as

Simon Bartlmae, Andreas Hene, Joshua Könen, and Heiko Röglin. Parameterized Algorithms for the Drone Delivery Problem. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bartlmae_et_al:LIPIcs.ISAAC.2025.8,
  author =	{Bartlmae, Simon and Hene, Andreas and K\"{o}nen, Joshua and R\"{o}glin, Heiko},
  title =	{{Parameterized Algorithms for the Drone Delivery Problem}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.8},
  URN =		{urn:nbn:de:0030-drops-249162},
  doi =		{10.4230/LIPIcs.ISAAC.2025.8},
  annote =	{Keywords: Complexity, Delivery, FPT algorithms, Graph Theory}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.27
On the h-Majority Dynamics with Many Opinions

Authors: Francesco d'Amore, Niccolò D'Archivio, George Giakkoupis, and Emanuele Natale

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
We present the first upper bound on the convergence time to consensus of the well-known h-majority dynamics with k opinions, in the synchronous setting, for h and k that are both non-constant values. We suppose that, at the beginning of the process, there is some initial additive bias towards some plurality opinion, that is, there is an opinion that is supported by x nodes while any other opinion is supported by strictly fewer nodes. We prove that, with high probability, if the bias is ω(√x) and the initial plurality opinion is supported by at least x = ω(log n) nodes, then the process converges to plurality consensus in O(log n) rounds whenever h = ω(n log n / x). A main corollary is the following: if k = o(n / log n) and the process starts from an almost-balanced configuration with an initial bias of magnitude ω(√{n/k}) towards the initial plurality opinion, then any function h = ω(k log n) suffices to guarantee convergence to consensus in O(log n) rounds, with high probability. Our upper bound shows that the lower bound of Ω(k / h²) rounds to reach consensus given by Becchetti et al. (2017) cannot be pushed further than Ω̃(k / h). Moreover, the bias we require is asymptotically smaller than the Ω(√{nlog n}) bias that guarantees plurality consensus in the 3-majority dynamics: in our case, the required bias is at most any (arbitrarily small) function in ω(√x) for any value of k ≥ 2.
Cite as

Francesco d'Amore, Niccolò D'Archivio, George Giakkoupis, and Emanuele Natale. On the h-Majority Dynamics with Many Opinions. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 27:1-27:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{damore_et_al:LIPIcs.DISC.2025.27,
  author =	{d'Amore, Francesco and D'Archivio, Niccol\`{o} and Giakkoupis, George and Natale, Emanuele},
  title =	{{On the h-Majority Dynamics with Many Opinions}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{27:1--27:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.27},
  URN =		{urn:nbn:de:0030-drops-248448},
  doi =		{10.4230/LIPIcs.DISC.2025.27},
  annote =	{Keywords: Distributed Algorithms, Randomized Algorithms, Markov Chains, Consensus Problem, Opinion dynamics, Plurality Consensus}
}
Document
DOI: 10.4230/LIPIcs.TIME.2025.5
Higher-Order Timed Automata and Tail Recursion

Authors: Florian Bruse

Published in: LIPIcs, Volume 355, 32nd International Symposium on Temporal Representation and Reasoning (TIME 2025)

Abstract
Timed Automata (TA) are a popular formalism to model systems in dense linear time. However, due to their finite state-space, they can only model systems with a finitary logical behavior. There are extensions to e.g., timed pushdown systems and timed recursive state machines. Higher-Order Recursion Schemes (HORS) are another popular model for infinite-state, non-regular systems, naturally stratified by their type-theoretic order. We recently introduced Real-Time Recursion schemes as an approximation of HORS to real-time systems. This paper updates Real-Time Recursion Schemes into Higher-Order Timed Automata, a formalism that defines a tree-shaped timed automaton, which is more suitable to model actual systems. We show that the model-checking problem against the timed version of the modal mu-calculus exhibits the expected complexity bounds, i.e., an increase by one exponential towards the untimed version. We also show that, in the presence of tail recursion, half an exponential can be recovered, mirroring similar gains in the untimed setting. We also give a matching lower bound for the special case of order-1 HORTA. We conjecture that this can be generalized for all orders.
Cite as

Florian Bruse. Higher-Order Timed Automata and Tail Recursion. In 32nd International Symposium on Temporal Representation and Reasoning (TIME 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 355, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bruse:LIPIcs.TIME.2025.5,
  author =	{Bruse, Florian},
  title =	{{Higher-Order Timed Automata and Tail Recursion}},
  booktitle =	{32nd International Symposium on Temporal Representation and Reasoning (TIME 2025)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-401-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{355},
  editor =	{Vidal, Thierry and Wa{\l}\k{e}ga, Przemys{\l}aw Andrzej},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2025.5},
  URN =		{urn:nbn:de:0030-drops-244519},
  doi =		{10.4230/LIPIcs.TIME.2025.5},
  annote =	{Keywords: Timed Automata, Higher-Order Recursion Schemes, Tree Automata, Tail Recursion}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.93
Recognizing and Realizing Temporal Reachability Graphs

Authors: Thomas Erlebach, Othon Michail, and Nils Morawietz

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
A temporal graph 𝒢 = (G,λ) can be represented by an underlying graph G = (V,E) together with a function λ that assigns to each edge e ∈ E the set of time steps during which e is present. The reachability graph of 𝒢 is the directed graph D = (V,A) with (u,v) ∈ A if and only if there is a temporal path from u to v. We study the Reachability Graph Realizability (RGR) problem that asks whether a given directed graph D = (V,A) is the reachability graph of some temporal graph. The question can be asked for undirected or directed temporal graphs, for reachability defined via strict or non-strict temporal paths, and with or without restrictions on λ (simple, proper, or both). Answering an open question posed by Casteigts et al. (TCS 2024), we show that all variants of the problem are NP-complete, except for two variants that become trivial in the directed case. For undirected temporal graphs, we consider the complexity of the problem with respect to the solid graph, that is, the graph containing all edges that could potentially receive a label in any realization. We show that the RGR problem is fixed-parameter tractable for the feedback edge set number of the solid graph. As we show, the latter parameter can presumably not be replaced by smaller parameters like feedback vertex set number or treedepth, since the problem is W[2]-hard for them.
Cite as

Thomas Erlebach, Othon Michail, and Nils Morawietz. Recognizing and Realizing Temporal Reachability Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 93:1-93:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{erlebach_et_al:LIPIcs.ESA.2025.93,
  author =	{Erlebach, Thomas and Michail, Othon and Morawietz, Nils},
  title =	{{Recognizing and Realizing Temporal Reachability Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{93:1--93:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.93},
  URN =		{urn:nbn:de:0030-drops-245627},
  doi =		{10.4230/LIPIcs.ESA.2025.93},
  annote =	{Keywords: parameterized complexity, temporal graphs, FPT algorithm, feedback edge set, directed graph recognition}
}
Document
DOI: 10.4230/LIPIcs.TQC.2025.1
Quantum Search with In-Place Queries

Authors: Blake Holman, Ronak Ramachandran, and Justin Yirka

Published in: LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)

Abstract
Quantum query complexity is typically characterized in terms of xor queries |x,y⟩ ↦ |x,y⊕ f(x)⟩ or phase queries, which ensure that even queries to non-invertible functions are unitary. When querying a permutation, another natural model is unitary: in-place queries |x⟩↦ |f(x)⟩. Some problems are known to require exponentially fewer in-place queries than xor queries, but no separation has been shown in the opposite direction. A candidate for such a separation was the problem of inverting a permutation over N elements. This task, equivalent to unstructured search in the context of permutations, is solvable with O(√N) xor queries but was conjectured to require Ω(N) in-place queries. We refute this conjecture by designing a quantum algorithm for Permutation Inversion using O(√N) in-place queries. Our algorithm achieves the same speedup as Grover’s algorithm despite the inability to efficiently uncompute queries or perform straightforward oracle-controlled reflections. Nonetheless, we show that there are indeed problems which require fewer xor queries than in-place queries. We introduce a subspace-conversion problem called Function Erasure that requires 1 xor query and Θ(√N) in-place queries. Then, we build on a recent extension of the quantum adversary method to characterize exact conditions for a decision problem to exhibit such a separation, and we propose a candidate problem.
Cite as

Blake Holman, Ronak Ramachandran, and Justin Yirka. Quantum Search with In-Place Queries. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{holman_et_al:LIPIcs.TQC.2025.1,
  author =	{Holman, Blake and Ramachandran, Ronak and Yirka, Justin},
  title =	{{Quantum Search with In-Place Queries}},
  booktitle =	{20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
  pages =	{1:1--1:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-392-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{350},
  editor =	{Fefferman, Bill},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.1},
  URN =		{urn:nbn:de:0030-drops-240502},
  doi =		{10.4230/LIPIcs.TQC.2025.1},
  annote =	{Keywords: Quantum algorithms, query complexity, quantum complexity theory, quantum search, Grover’s algorithm, permutation inversion}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.62
The Complexity of Reachability Problems in Strongly Connected Finite Automata

Authors: Stefan Kiefer and Andrew Ryzhikov

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Several reachability problems in finite automata, such as completeness of NFAs and synchronisation of total DFAs, correspond to fundamental properties of sets of nonnegative matrices. In particular, the two mentioned properties correspond to matrix mortality and ergodicity, which ask whether there exists a product of the input matrices that is equal to, respectively, the zero matrix and a matrix with a column of strictly positive entries only. The case where the input automaton is strongly connected (that is, the corresponding set of nonnegative matrices is irreducible) frequently appears in applications and often admits better properties than the general case. In this paper, we address the existence of such properties from the computational complexity point of view, and develop a versatile technique to show that several NL-complete problems remain NL-complete in the strongly connected case. In particular, we show that deciding if a binary total DFA is synchronising is NL-complete even if it is promised to be strongly connected, and that deciding completeness of a binary unambiguous NFA with very limited nondeterminism is NL-complete under the same promise.
Cite as

Stefan Kiefer and Andrew Ryzhikov. The Complexity of Reachability Problems in Strongly Connected Finite Automata. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 62:1-62:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kiefer_et_al:LIPIcs.MFCS.2025.62,
  author =	{Kiefer, Stefan and Ryzhikov, Andrew},
  title =	{{The Complexity of Reachability Problems in Strongly Connected Finite Automata}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{62:1--62:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.62},
  URN =		{urn:nbn:de:0030-drops-241690},
  doi =		{10.4230/LIPIcs.MFCS.2025.62},
  annote =	{Keywords: unambiguous automata, nonnegative matrices, irreducible matrix sets, strongly connected automata, matrix monoids, mortality, completeness, synchronisation, ergodicity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.67
#SAT-Algorithms for Classes of Threshold Circuits Based on Probabilistic Rank

Authors: Nutan Limaye, Adarsh Srinivasan, and Srikanth Srinivasan

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
There is a large body of work that shows how to leverage lower bound techniques for circuit classes to obtain satisfiability algorithms that run in better than brute-force time [Ramamohan Paturi et al., 1997; Ryan Williams, 2014]. For circuits with threshold gates, there are several such algorithms based on either - Probabilistic Representations by low-degree polynomials, which allow for the use of fast polynomial evaluation algorithms, or - Low rank, which allows for an efficient reduction to rectangular matrix multiplication. In this paper, we use a related notion of probabilistic rank to obtain satisfiability algorithms for circuit classes contained in ACC⁰∘3-PTF, i.e. constant-depth circuits with modular counting gates and a single layer of degree-3 polynomial threshold functions. Even for the special case of a single 3-PTF, it is not clear how to use either of the above two strategies to get a non-trivial satisfiability algorithm. The best known algorithm in this case previously was based on memoization and yields worse guarantees than our algorithm.
Cite as

Nutan Limaye, Adarsh Srinivasan, and Srikanth Srinivasan. #SAT-Algorithms for Classes of Threshold Circuits Based on Probabilistic Rank. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 67:1-67:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{limaye_et_al:LIPIcs.MFCS.2025.67,
  author =	{Limaye, Nutan and Srinivasan, Adarsh and Srinivasan, Srikanth},
  title =	{{#SAT-Algorithms for Classes of Threshold Circuits Based on Probabilistic Rank}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{67:1--67:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.67},
  URN =		{urn:nbn:de:0030-drops-241744},
  doi =		{10.4230/LIPIcs.MFCS.2025.67},
  annote =	{Keywords: probabilistic polynomials, probabilistic rank, circuit satisfiability, circuit lower bounds, polynomial method, threshold circuits}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.14
Register Automata with Permutations

Authors: Mrudula Balachander, Emmanuel Filiot, Raffaella Gentilini, and Nikos Tzevelekos

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We propose Permutation Deterministic Register Automata (pDRAs), a deterministic register automaton model where we allow permutations of registers in transitions. The model enables minimal canonical representations and pDRAs can be tested for equivalence in polynomial time. The complexity of minimization is between GI (the complexity of graph isomorphism) and NP. We then introduce a subclass of pDRAs, called register automata with fixed permutation policy, where the register permutation discipline is stipulated globally. This class generalizes the model proposed by Benedikt, Ley and Puppis in 2010, and we show that it also admits minimal and canonical representations, based on a finite-index word equivalence relation. As an application, we show that for any regular data language L, the minimal register automaton with fixed permutation policy recognizing L can be actively learned in polynomial time using oracles for membership, equivalence and data-memorability queries. We show that all the oracles can be implemented in polynomial time, and so this yields a polynomial time minimization algorithm.
Cite as

Mrudula Balachander, Emmanuel Filiot, Raffaella Gentilini, and Nikos Tzevelekos. Register Automata with Permutations. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balachander_et_al:LIPIcs.MFCS.2025.14,
  author =	{Balachander, Mrudula and Filiot, Emmanuel and Gentilini, Raffaella and Tzevelekos, Nikos},
  title =	{{Register Automata with Permutations}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.14},
  URN =		{urn:nbn:de:0030-drops-241219},
  doi =		{10.4230/LIPIcs.MFCS.2025.14},
  annote =	{Keywords: Register automata, data words, equivalence, minimization, active learning}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.92
On Piecewise Affine Reachability with Bellman Operators

Authors: Anton Varonka and Kazuki Watanabe

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
A piecewise affine map is one of the simplest mathematical objects exhibiting complex dynamics. The reachability problem of piecewise affine maps is as follows: Given two vectors s, t ∈ ℚ^d and a piecewise affine map f: ℚ^d → ℚ^d, is there n ∈ ℕ such that fⁿ(s) = t? Koiran, Cosnard, and Garzon show that the reachability problem of piecewise affine maps is undecidable even in dimension 2. Most of the recent progress has been focused on decision procedures for one-dimensional piecewise affine maps, where the reachability problem has been shown to be decidable for some subclasses. However, the general undecidability discouraged research into positive results in arbitrary dimension. In this work, we investigate a rich subclass of piecewise affine maps arising as Bellman operators of Markov decision processes (MDPs). We consider the reachability problem restricted to this subclass and examine its decidability in arbitrary dimensions. We establish that the reachability problem for Bellman operators is decidable in any dimension under either of the following conditions: (i) the target vector t is not the fixed point of the operator f; or (ii) the initial and target vectors s and t are comparable with respect to the componentwise order. Furthermore, we show that the reachability problem for two-dimensional Bellman operators is decidable for arbitrary s, t ∈ ℚ^d, in contrast to the known undecidability of reachability for general piecewise affine maps.
Cite as

Anton Varonka and Kazuki Watanabe. On Piecewise Affine Reachability with Bellman Operators. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 92:1-92:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{varonka_et_al:LIPIcs.MFCS.2025.92,
  author =	{Varonka, Anton and Watanabe, Kazuki},
  title =	{{On Piecewise Affine Reachability with Bellman Operators}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{92:1--92:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.92},
  URN =		{urn:nbn:de:0030-drops-241998},
  doi =		{10.4230/LIPIcs.MFCS.2025.92},
  annote =	{Keywords: piecewise affine map, reachability, value iteration, Markov decision process, Bellman operator}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.38
The Complexity of Separability for Semilinear Sets and Parikh Automata

Authors: Elias Rojas Collins, Chris Köcher, and Georg Zetzsche

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
In a separability problem, we are given two sets K and L from a class 𝒞, and we want to decide whether there exists a set S from a class 𝒮 such that K ⊆ S and S ∩ L = ∅. In this case, we speak of separability of sets in 𝒞 by sets in 𝒮. We study two types of separability problems. First, we consider separability of semilinear sets (i.e. subsets of ℕ^d for some d) by sets definable by quantifier-free monadic Presburger formulas (or equivalently, the recognizable subsets of ℕ^d). Here, a formula is monadic if each atom uses at most one variable. Second, we consider separability of languages of Parikh automata by regular languages. A Parikh automaton is a machine with access to counters that can only be incremented, and have to meet a semilinear constraint at the end of the run. Both of these separability problems are known to be decidable with elementary complexity. Our main results are that both problems are coNP-complete. In the case of semilinear sets, coNP-completeness holds regardless of whether the input sets are specified by existential Presburger formulas, quantifier-free formulas, or semilinear representations. Our results imply that recognizable separability of rational subsets of Σ* × ℕ^d (shown decidable by Choffrut and Grigorieff) is coNP-complete as well. Another application is that regularity of deterministic Parikh automata (where the target set is specified using a quantifier-free Presburger formula) is coNP-complete as well.
Cite as

Elias Rojas Collins, Chris Köcher, and Georg Zetzsche. The Complexity of Separability for Semilinear Sets and Parikh Automata. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 38:1-38:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{collins_et_al:LIPIcs.MFCS.2025.38,
  author =	{Collins, Elias Rojas and K\"{o}cher, Chris and Zetzsche, Georg},
  title =	{{The Complexity of Separability for Semilinear Sets and Parikh Automata}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{38:1--38:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.38},
  URN =		{urn:nbn:de:0030-drops-241457},
  doi =		{10.4230/LIPIcs.MFCS.2025.38},
  annote =	{Keywords: Vector Addition System, Separability, Regular Language}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.75
Temporal Graph Realization with Bounded Stretch

Authors: George B. Mertzios, Hendrik Molter, Nils Morawietz, and Paul G. Spirakis

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
A periodic temporal graph, in its simplest form, is a graph in which every edge appears exactly once in the first Δ time steps, and then it reappears recurrently every Δ time steps, where Δ is a given period length. This model offers a natural abstraction of transportation networks where each transportation link connects two destinations periodically. From a network design perspective, a crucial task is to assign the time-labels on the edges in a way that optimizes some criterion. In this paper we introduce a very natural optimality criterion that captures how the temporal distances of all vertex pairs are "stretched", compared to their physical distances, i.e. their distances in the underlying static (non-temporal) graph. Given a static graph G, the task is to assign to each edge one time-label between 1 and Δ such that, in the resulting periodic temporal graph with period Δ, the duration of the fastest temporal path from any vertex u to any other vertex v is at most α times the distance between u and v in G. Here, the value of α measures how much the shortest paths are allowed to be stretched once we assign the periodic time-labels. Our results span three different directions: First, we provide a series of approximation and NP-hardness results. Second, we provide approximation and fixed-parameter algorithms. Among them, we provide a simple polynomial-time algorithm (the radius-algorithm) which always guarantees an approximation strictly smaller than Δ, and which also computes the optimum stretch in some cases. Third, we consider a parameterized local search extension of the problem where we are given the temporal labeling of the graph, but we are allowed to change the time-labels of at most k edges; for this problem we prove that it is W[2]-hard but admits an XP algorithm with respect to k.
Cite as

George B. Mertzios, Hendrik Molter, Nils Morawietz, and Paul G. Spirakis. Temporal Graph Realization with Bounded Stretch. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 75:1-75:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mertzios_et_al:LIPIcs.MFCS.2025.75,
  author =	{Mertzios, George B. and Molter, Hendrik and Morawietz, Nils and Spirakis, Paul G.},
  title =	{{Temporal Graph Realization with Bounded Stretch}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{75:1--75:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.75},
  URN =		{urn:nbn:de:0030-drops-241829},
  doi =		{10.4230/LIPIcs.MFCS.2025.75},
  annote =	{Keywords: Temporal graph, periodic temporal labeling, fastest temporal path, graph realization, temporal connectivity, stretch}
}
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