29 Search Results for "Göös, Mika"


Document
RANDOM
Sampling and Certifying Symmetric Functions

Authors: Yuval Filmus, Itai Leigh, Artur Riazanov, and Dmitry Sokolov

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)


Abstract
A circuit 𝒞 samples a distribution X with an error ε if the statistical distance between the output of 𝒞 on the uniform input and X is ε. We study the hardness of sampling a uniform distribution over the set of n-bit strings of Hamming weight k denoted by Uⁿ_k for decision forests, i.e. every output bit is computed as a decision tree of the inputs. For every k there is an O(log n)-depth decision forest sampling Uⁿ_k with an inverse-polynomial error [Emanuele Viola, 2012; Czumaj, 2015]. We show that for every ε > 0 there exists τ such that for decision depth τ log (n/k) / log log (n/k), the error for sampling U_kⁿ is at least 1-ε. Our result is based on the recent robust sunflower lemma [Ryan Alweiss et al., 2021; Rao, 2019]. Our second result is about matching a set of n-bit strings with the image of a d-local circuit, i.e. such that each output bit depends on at most d input bits. We study the set of all n-bit strings whose Hamming weight is at least n/2. We improve the previously known locality lower bound from Ω(log^* n) [Beyersdorff et al., 2013] to Ω(√log n), leaving only a quartic gap from the best upper bound of O(log² n).

Cite as

Yuval Filmus, Itai Leigh, Artur Riazanov, and Dmitry Sokolov. Sampling and Certifying Symmetric Functions. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 36:1-36:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{filmus_et_al:LIPIcs.APPROX/RANDOM.2023.36,
  author =	{Filmus, Yuval and Leigh, Itai and Riazanov, Artur and Sokolov, Dmitry},
  title =	{{Sampling and Certifying Symmetric Functions}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{36:1--36:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.36},
  URN =		{urn:nbn:de:0030-drops-188611},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.36},
  annote =	{Keywords: sampling, lower bounds, robust sunflowers, decision trees, switching networks}
}
Document
Depth-3 Circuits for Inner Product

Authors: Mika Göös, Ziyi Guan, and Tiberiu Mosnoi

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)


Abstract
What is the Σ₃²-circuit complexity (depth 3, bottom-fanin 2) of the 2n-bit inner product function? The complexity is known to be exponential 2^{α_n n} for some α_n = Ω(1). We show that the limiting constant α := lim sup α_n satisfies 0.847... ≤ α ≤ 0.965... . Determining α is one of the seemingly-simplest open problems about depth-3 circuits. The question was recently raised by Golovnev, Kulikov, and Williams (ITCS 2021) and Frankl, Gryaznov, and Talebanfard (ITCS 2022), who observed that α ∈ [0.5,1]. To obtain our improved bounds, we analyse a covering LP that captures the Σ₃²-complexity up to polynomial factors. In particular, our lower bound is proved by constructing a feasible solution to the dual LP.

Cite as

Mika Göös, Ziyi Guan, and Tiberiu Mosnoi. Depth-3 Circuits for Inner Product. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 51:1-51:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{goos_et_al:LIPIcs.MFCS.2023.51,
  author =	{G\"{o}\"{o}s, Mika and Guan, Ziyi and Mosnoi, Tiberiu},
  title =	{{Depth-3 Circuits for Inner Product}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{51:1--51:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.51},
  URN =		{urn:nbn:de:0030-drops-185856},
  doi =		{10.4230/LIPIcs.MFCS.2023.51},
  annote =	{Keywords: Circuit complexity, inner product}
}
Document
Track A: Algorithms, Complexity and Games
Online Learning and Disambiguations of Partial Concept Classes

Authors: Tsun-Ming Cheung, Hamed Hatami, Pooya Hatami, and Kaave Hosseini

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)


Abstract
In a recent article, Alon, Hanneke, Holzman, and Moran (FOCS '21) introduced a unifying framework to study the learnability of classes of partial concepts. One of the central questions studied in their work is whether the learnability of a partial concept class is always inherited from the learnability of some "extension" of it to a total concept class. They showed this is not the case for PAC learning but left the problem open for the stronger notion of online learnability. We resolve this problem by constructing a class of partial concepts that is online learnable, but no extension of it to a class of total concepts is online learnable (or even PAC learnable).

Cite as

Tsun-Ming Cheung, Hamed Hatami, Pooya Hatami, and Kaave Hosseini. Online Learning and Disambiguations of Partial Concept Classes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 42:1-42:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{cheung_et_al:LIPIcs.ICALP.2023.42,
  author =	{Cheung, Tsun-Ming and Hatami, Hamed and Hatami, Pooya and Hosseini, Kaave},
  title =	{{Online Learning and Disambiguations of Partial Concept Classes}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{42:1--42:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.42},
  URN =		{urn:nbn:de:0030-drops-180946},
  doi =		{10.4230/LIPIcs.ICALP.2023.42},
  annote =	{Keywords: Online learning, Littlestone dimension, VC dimension, partial concept class, clique vs independent set, Alon-Saks-Seymour conjecture, Standard Optimal Algorithm, PAC learning}
}
Document
TFNP Characterizations of Proof Systems and Monotone Circuits

Authors: Sam Buss, Noah Fleming, and Russell Impagliazzo

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)


Abstract
Connections between proof complexity and circuit complexity have become major tools for obtaining lower bounds in both areas. These connections - which take the form of interpolation theorems and query-to-communication lifting theorems - translate efficient proofs into small circuits, and vice versa, allowing tools from one area to be applied to the other. Recently, the theory of TFNP has emerged as a unifying framework underlying these connections. For many of the proof systems which admit such a connection there is a TFNP problem which characterizes it: the class of problems which are reducible to this TFNP problem via query-efficient reductions is equivalent to the tautologies that can be efficiently proven in the system. Through this, proof complexity has become a major tool for proving separations in black-box TFNP. Similarly, for certain monotone circuit models, the class of functions that it can compute efficiently is equivalent to what can be reduced to a certain TFNP problem in a communication-efficient manner. When a TFNP problem has both a proof and circuit characterization, one can prove an interpolation theorem. Conversely, many lifting theorems can be viewed as relating the communication and query reductions to TFNP problems. This is exciting, as it suggests that TFNP provides a roadmap for the development of further interpolation theorems and lifting theorems. In this paper we begin to develop a more systematic understanding of when these connections to TFNP occur. We give exact conditions under which a proof system or circuit model admits a characterization by a TFNP problem. We show: - Every well-behaved proof system which can prove its own soundness (a reflection principle) is characterized by a TFNP problem. Conversely, every TFNP problem gives rise to a well-behaved proof system which proves its own soundness. - Every well-behaved monotone circuit model which admits a universal family of functions is characterized by a TFNP problem. Conversely, every TFNP problem gives rise to a well-behaved monotone circuit model with a universal problem. As an example, we provide a TFNP characterization of the Polynomial Calculus, answering a question from [Mika Göös et al., 2022], and show that it can prove its own soundness.

Cite as

Sam Buss, Noah Fleming, and Russell Impagliazzo. TFNP Characterizations of Proof Systems and Monotone Circuits. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 30:1-30:40, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{buss_et_al:LIPIcs.ITCS.2023.30,
  author =	{Buss, Sam and Fleming, Noah and Impagliazzo, Russell},
  title =	{{TFNP Characterizations of Proof Systems and Monotone Circuits}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{30:1--30:40},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.30},
  URN =		{urn:nbn:de:0030-drops-175332},
  doi =		{10.4230/LIPIcs.ITCS.2023.30},
  annote =	{Keywords: Proof Complexity, Circuit Complexity, TFNP}
}
Document
RANDOM
Communication Complexity of Collision

Authors: Mika Göös and Siddhartha Jain

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)


Abstract
The Collision problem is to decide whether a given list of numbers (x_1,…,x_n) ∈ [n]ⁿ is 1-to-1 or 2-to-1 when promised one of them is the case. We show an n^Ω(1) randomised communication lower bound for the natural two-party version of Collision where Alice holds the first half of the bits of each x_i and Bob holds the second half. As an application, we also show a similar lower bound for a weak bit-pigeonhole search problem, which answers a question of Itsykson and Riazanov (CCC 2021).

Cite as

Mika Göös and Siddhartha Jain. Communication Complexity of Collision. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 19:1-19:9, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{goos_et_al:LIPIcs.APPROX/RANDOM.2022.19,
  author =	{G\"{o}\"{o}s, Mika and Jain, Siddhartha},
  title =	{{Communication Complexity of Collision}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{19:1--19:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.19},
  URN =		{urn:nbn:de:0030-drops-171415},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.19},
  annote =	{Keywords: Collision, Communication complexity, Lifting}
}
Document
Further Collapses in TFNP

Authors: Mika Göös, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre, William Pires, Robert Robere, and Ran Tao

Published in: LIPIcs, Volume 234, 37th Computational Complexity Conference (CCC 2022)


Abstract
We show EOPL = PLS ∩ PPAD. Here the class EOPL consists of all total search problems that reduce to the End-of-Potential-Line problem, which was introduced in the works by Hubáček and Yogev (SICOMP 2020) and Fearnley et al. (JCSS 2020). In particular, our result yields a new simpler proof of the breakthrough collapse CLS = PLS ∩ PPAD by Fearnley et al. (STOC 2021). We also prove a companion result SOPL = PLS ∩ PPADS, where SOPL is the class associated with the Sink-of-Potential-Line problem.

Cite as

Mika Göös, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre, William Pires, Robert Robere, and Ran Tao. Further Collapses in TFNP. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 33:1-33:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{goos_et_al:LIPIcs.CCC.2022.33,
  author =	{G\"{o}\"{o}s, Mika and Hollender, Alexandros and Jain, Siddhartha and Maystre, Gilbert and Pires, William and Robere, Robert and Tao, Ran},
  title =	{{Further Collapses in TFNP}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{33:1--33:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-241-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{234},
  editor =	{Lovett, Shachar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.33},
  URN =		{urn:nbn:de:0030-drops-165954},
  doi =		{10.4230/LIPIcs.CCC.2022.33},
  annote =	{Keywords: TFNP, PPAD, PLS, EOPL}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Lower Bounds for Unambiguous Automata via Communication Complexity

Authors: Mika Göös, Stefan Kiefer, and Weiqiang Yuan

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)


Abstract
We use results from communication complexity, both new and old ones, to prove lower bounds for unambiguous finite automata (UFAs). We show three results. 1) Complement: There is a language L recognised by an n-state UFA such that the complement language ̅L requires NFAs with n^Ω̃(log n) states. This improves on a lower bound by Raskin. 2) Union: There are languages L₁, L₂ recognised by n-state UFAs such that the union L₁∪L₂ requires UFAs with n^Ω̃(log n) states. 3) Separation: There is a language L such that both L and ̅L are recognised by n-state NFAs but such that L requires UFAs with n^Ω(log n) states. This refutes a conjecture by Colcombet.

Cite as

Mika Göös, Stefan Kiefer, and Weiqiang Yuan. Lower Bounds for Unambiguous Automata via Communication Complexity. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 126:1-126:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{goos_et_al:LIPIcs.ICALP.2022.126,
  author =	{G\"{o}\"{o}s, Mika and Kiefer, Stefan and Yuan, Weiqiang},
  title =	{{Lower Bounds for Unambiguous Automata via Communication Complexity}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{126:1--126:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.126},
  URN =		{urn:nbn:de:0030-drops-164679},
  doi =		{10.4230/LIPIcs.ICALP.2022.126},
  annote =	{Keywords: Unambiguous automata, communication complexity}
}
Document
On Semi-Algebraic Proofs and Algorithms

Authors: Noah Fleming, Mika Göös, Stefan Grosser, and Robert Robere

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)


Abstract
We give a new characterization of the Sherali-Adams proof system, showing that there is a degree-d Sherali-Adams refutation of an unsatisfiable CNF formula C if and only if there is an ε > 0 and a degree-d conical junta J such that viol_C(x) - ε = J, where viol_C(x) counts the number of falsified clauses of C on an input x. Using this result we show that the linear separation complexity, a complexity measure recently studied by Hrubeš (and independently by de Oliveira Oliveira and Pudlák under the name of weak monotone linear programming gates), monotone feasibly interpolates Sherali-Adams proofs. We then investigate separation results for viol_C(x) - ε. In particular, we give a family of unsatisfiable CNF formulas C which have polynomial-size and small-width resolution proofs, but for which any representation of viol_C(x) - 1 by a conical junta requires degree Ω(n); this resolves an open question of Filmus, Mahajan, Sood, and Vinyals. Since Sherali-Adams can simulate resolution, this separates the non-negative degree of viol_C(x) - 1 and viol_C(x) - ε for arbitrarily small ε > 0. Finally, by applying lifting theorems, we translate this lower bound into new separation results between extension complexity and monotone circuit complexity.

Cite as

Noah Fleming, Mika Göös, Stefan Grosser, and Robert Robere. On Semi-Algebraic Proofs and Algorithms. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 69:1-69:25, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{fleming_et_al:LIPIcs.ITCS.2022.69,
  author =	{Fleming, Noah and G\"{o}\"{o}s, Mika and Grosser, Stefan and Robere, Robert},
  title =	{{On Semi-Algebraic Proofs and Algorithms}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{69:1--69:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.69},
  URN =		{urn:nbn:de:0030-drops-156658},
  doi =		{10.4230/LIPIcs.ITCS.2022.69},
  annote =	{Keywords: Proof Complexity, Extended Formulations, Circuit Complexity, Sherali-Adams}
}
Document
On the Power and Limitations of Branch and Cut

Authors: Noah Fleming, Mika Göös, Russell Impagliazzo, Toniann Pitassi, Robert Robere, Li-Yang Tan, and Avi Wigderson

Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)


Abstract
The Stabbing Planes proof system [Paul Beame et al., 2018] was introduced to model the reasoning carried out in practical mixed integer programming solvers. As a proof system, it is powerful enough to simulate Cutting Planes and to refute the Tseitin formulas - certain unsatisfiable systems of linear equations od 2 - which are canonical hard examples for many algebraic proof systems. In a recent (and surprising) result, Dadush and Tiwari [Daniel Dadush and Samarth Tiwari, 2020] showed that these short refutations of the Tseitin formulas could be translated into quasi-polynomial size and depth Cutting Planes proofs, refuting a long-standing conjecture. This translation raises several interesting questions. First, whether all Stabbing Planes proofs can be efficiently simulated by Cutting Planes. This would allow for the substantial analysis done on the Cutting Planes system to be lifted to practical mixed integer programming solvers. Second, whether the quasi-polynomial depth of these proofs is inherent to Cutting Planes. In this paper we make progress towards answering both of these questions. First, we show that any Stabbing Planes proof with bounded coefficients (SP*) can be translated into Cutting Planes. As a consequence of the known lower bounds for Cutting Planes, this establishes the first exponential lower bounds on SP*. Using this translation, we extend the result of Dadush and Tiwari to show that Cutting Planes has short refutations of any unsatisfiable system of linear equations over a finite field. Like the Cutting Planes proofs of Dadush and Tiwari, our refutations also incur a quasi-polynomial blow-up in depth, and we conjecture that this is inherent. As a step towards this conjecture, we develop a new geometric technique for proving lower bounds on the depth of Cutting Planes proofs. This allows us to establish the first lower bounds on the depth of Semantic Cutting Planes proofs of the Tseitin formulas.

Cite as

Noah Fleming, Mika Göös, Russell Impagliazzo, Toniann Pitassi, Robert Robere, Li-Yang Tan, and Avi Wigderson. On the Power and Limitations of Branch and Cut. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 6:1-6:30, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{fleming_et_al:LIPIcs.CCC.2021.6,
  author =	{Fleming, Noah and G\"{o}\"{o}s, Mika and Impagliazzo, Russell and Pitassi, Toniann and Robere, Robert and Tan, Li-Yang and Wigderson, Avi},
  title =	{{On the Power and Limitations of Branch and Cut}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{6:1--6:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.6},
  URN =		{urn:nbn:de:0030-drops-142809},
  doi =		{10.4230/LIPIcs.CCC.2021.6},
  annote =	{Keywords: Proof Complexity, Integer Programming, Cutting Planes, Branch and Cut, Stabbing Planes}
}
Document
A Majority Lemma for Randomised Query Complexity

Authors: Mika Göös and Gilbert Maystre

Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)


Abstract
We show that computing the majority of n copies of a boolean function g has randomised query complexity R(Maj∘gⁿ) = Θ(n⋅R ̅_{1/n}(g)). In fact, we show that to obtain a similar result for any composed function f∘gⁿ, it suffices to prove a sufficiently strong form of the result only in the special case g = GapOr.

Cite as

Mika Göös and Gilbert Maystre. A Majority Lemma for Randomised Query Complexity. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 18:1-18:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{goos_et_al:LIPIcs.CCC.2021.18,
  author =	{G\"{o}\"{o}s, Mika and Maystre, Gilbert},
  title =	{{A Majority Lemma for Randomised Query Complexity}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{18:1--18:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.18},
  URN =		{urn:nbn:de:0030-drops-142922},
  doi =		{10.4230/LIPIcs.CCC.2021.18},
  annote =	{Keywords: Query Complexity, Composition, Majority}
}
Document
On Query-To-Communication Lifting for Adversary Bounds

Authors: Anurag Anshu, Shalev Ben-David, and Srijita Kundu

Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)


Abstract
We investigate query-to-communication lifting theorems for models related to the quantum adversary bounds. Our results are as follows: 1) We show that the classical adversary bound lifts to a lower bound on randomized communication complexity with a constant-sized gadget. We also show that the classical adversary bound is a strictly stronger lower bound technique than the previously-lifted measure known as critical block sensitivity, making our lifting theorem one of the strongest lifting theorems for randomized communication complexity using a constant-sized gadget. 2) Turning to quantum models, we show a connection between lifting theorems for quantum adversary bounds and secure 2-party quantum computation in a certain "honest-but-curious" model. Under the assumption that such secure 2-party computation is impossible, we show that a simplified version of the positive-weight adversary bound lifts to a quantum communication lower bound using a constant-sized gadget. We also give an unconditional lifting theorem which lower bounds bounded-round quantum communication protocols. 3) Finally, we give some new results in query complexity. We show that the classical adversary and the positive-weight quantum adversary are quadratically related. We also show that the positive-weight quantum adversary is never larger than the square of the approximate degree. Both relations hold even for partial functions.

Cite as

Anurag Anshu, Shalev Ben-David, and Srijita Kundu. On Query-To-Communication Lifting for Adversary Bounds. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 30:1-30:39, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{anshu_et_al:LIPIcs.CCC.2021.30,
  author =	{Anshu, Anurag and Ben-David, Shalev and Kundu, Srijita},
  title =	{{On Query-To-Communication Lifting for Adversary Bounds}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{30:1--30:39},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.30},
  URN =		{urn:nbn:de:0030-drops-143042},
  doi =		{10.4230/LIPIcs.CCC.2021.30},
  annote =	{Keywords: Quantum computing, query complexity, communication complexity, lifting theorems, adversary method}
}
Document
Communication Memento: Memoryless Communication Complexity

Authors: Srinivasan Arunachalam and Supartha Podder

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)


Abstract
We study the communication complexity of computing functions F: {0,1}ⁿ × {0,1}ⁿ → {0,1} in the memoryless communication model. Here, Alice is given x ∈ {0,1}ⁿ, Bob is given y ∈ {0,1}ⁿ and their goal is to compute F(x,y) subject to the following constraint: at every round, Alice receives a message from Bob and her reply to Bob solely depends on the message received and her input x (in particular, her reply is independent of the information from the previous rounds); the same applies to Bob. The cost of computing F in this model is the maximum number of bits exchanged in any round between Alice and Bob (on the worst case input x,y). In this paper, we also consider variants of our memoryless model wherein one party is allowed to have memory, the parties are allowed to communicate quantum bits, only one player is allowed to send messages. We show that some of these different variants of our memoryless communication model capture the garden-hose model of computation by Buhrman et al. (ITCS'13), space-bounded communication complexity by Brody et al. (ITCS'13) and the overlay communication complexity by Papakonstantinou et al. (CCC'14). Thus the memoryless communication complexity model provides a unified framework to study all these space-bounded communication complexity models. We establish the following main results: (1) We show that the memoryless communication complexity of F equals the logarithm of the size of the smallest bipartite branching program computing F (up to a factor 2); (2) We show that memoryless communication complexity equals garden-hose model of computation; (3) We exhibit various exponential separations between these memoryless communication models. We end with an intriguing open question: can we find an explicit function F and universal constant c > 1 for which the memoryless communication complexity is at least c log n? Note that c ≥ 2+ε would imply a Ω(n^{2+ε}) lower bound for general formula size, improving upon the best lower bound by [Nečiporuk, 1966].

Cite as

Srinivasan Arunachalam and Supartha Podder. Communication Memento: Memoryless Communication Complexity. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 61:1-61:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{arunachalam_et_al:LIPIcs.ITCS.2021.61,
  author =	{Arunachalam, Srinivasan and Podder, Supartha},
  title =	{{Communication Memento: Memoryless Communication Complexity}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{61:1--61:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.61},
  URN =		{urn:nbn:de:0030-drops-136007},
  doi =		{10.4230/LIPIcs.ITCS.2021.61},
  annote =	{Keywords: Communication complexity, space complexity, branching programs, garden-hose model, quantum computing}
}
Document
RANDOM
When Is Amplification Necessary for Composition in Randomized Query Complexity?

Authors: Shalev Ben-David, Mika Göös, Robin Kothari, and Thomas Watson

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)


Abstract
Suppose we have randomized decision trees for an outer function f and an inner function g. The natural approach for obtaining a randomized decision tree for the composed function (f∘ gⁿ)(x¹,…,xⁿ) = f(g(x¹),…,g(xⁿ)) involves amplifying the success probability of the decision tree for g, so that a union bound can be used to bound the error probability over all the coordinates. The amplification introduces a logarithmic factor cost overhead. We study the question: When is this log factor necessary? We show that when the outer function is parity or majority, the log factor can be necessary, even for models that are more powerful than plain randomized decision trees. Our results are related to, but qualitatively strengthen in various ways, known results about decision trees with noisy inputs.

Cite as

Shalev Ben-David, Mika Göös, Robin Kothari, and Thomas Watson. When Is Amplification Necessary for Composition in Randomized Query Complexity?. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 28:1-28:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bendavid_et_al:LIPIcs.APPROX/RANDOM.2020.28,
  author =	{Ben-David, Shalev and G\"{o}\"{o}s, Mika and Kothari, Robin and Watson, Thomas},
  title =	{{When Is Amplification Necessary for Composition in Randomized Query Complexity?}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{28:1--28:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.28},
  URN =		{urn:nbn:de:0030-drops-126316},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.28},
  annote =	{Keywords: Amplification, composition, query complexity}
}
Document
Limits of Preprocessing

Authors: Yuval Filmus, Yuval Ishai, Avi Kaplan, and Guy Kindler

Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)


Abstract
It is a classical result that the inner product function cannot be computed by an AC⁰ circuit [Merrick L. Furst et al., 1981; Miklós Ajtai, 1983; Johan Håstad, 1986]. It is conjectured that this holds even if we allow arbitrary preprocessing of each of the two inputs separately. We prove this conjecture when the preprocessing of one of the inputs is limited to output n + n/(log^{ω(1)} n) bits. Our methods extend to many other functions, including pseudorandom functions, and imply a (weak but nontrivial) limitation on the power of encoding inputs in low-complexity cryptography. Finally, under cryptographic assumptions, we relate the question of proving variants of the main conjecture with the question of learning AC⁰ under simple input distributions.

Cite as

Yuval Filmus, Yuval Ishai, Avi Kaplan, and Guy Kindler. Limits of Preprocessing. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 17:1-17:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{filmus_et_al:LIPIcs.CCC.2020.17,
  author =	{Filmus, Yuval and Ishai, Yuval and Kaplan, Avi and Kindler, Guy},
  title =	{{Limits of Preprocessing}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{17:1--17:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.17},
  URN =		{urn:nbn:de:0030-drops-125697},
  doi =		{10.4230/LIPIcs.CCC.2020.17},
  annote =	{Keywords: circuit, communication complexity, IPPP, preprocessing, PRF, simultaneous messages}
}
Document
On the Complexity of Modulo-q Arguments and the Chevalley - Warning Theorem

Authors: Mika Göös, Pritish Kamath, Katerina Sotiraki, and Manolis Zampetakis

Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)


Abstract
We study the search problem class PPA_q defined as a modulo-q analog of the well-known polynomial parity argument class PPA introduced by Papadimitriou (JCSS 1994). Our first result shows that this class can be characterized in terms of PPA_p for prime p. Our main result is to establish that an explicit version of a search problem associated to the Chevalley - Warning theorem is complete for PPA_p for prime p. This problem is natural in that it does not explicitly involve circuits as part of the input. It is the first such complete problem for PPA_p when p ≥ 3. Finally we discuss connections between Chevalley-Warning theorem and the well-studied short integer solution problem and survey the structural properties of PPA_q.

Cite as

Mika Göös, Pritish Kamath, Katerina Sotiraki, and Manolis Zampetakis. On the Complexity of Modulo-q Arguments and the Chevalley - Warning Theorem. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 19:1-19:42, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{goos_et_al:LIPIcs.CCC.2020.19,
  author =	{G\"{o}\"{o}s, Mika and Kamath, Pritish and Sotiraki, Katerina and Zampetakis, Manolis},
  title =	{{On the Complexity of Modulo-q Arguments and the Chevalley - Warning Theorem}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{19:1--19:42},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.19},
  URN =		{urn:nbn:de:0030-drops-125712},
  doi =		{10.4230/LIPIcs.CCC.2020.19},
  annote =	{Keywords: Total NP Search Problems, Modulo-q arguments, Chevalley - Warning Theorem}
}
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