22 Search Results for "Fran�ois, Nathana�l"

Document
DOI: 10.4230/LIPIcs.CONCUR.2023.13
Universal Quantification Makes Automatic Structures Hard to Decide

Authors: Christoph Haase and Radosław Piórkowski

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract
Automatic structures are structures whose universe and relations can be represented as regular languages. It follows from the standard closure properties of regular languages that the first-order theory of an automatic structure is decidable. While existential quantifiers can be eliminated in linear time by application of a homomorphism, universal quantifiers are commonly eliminated via the identity ∀x.Φ≡¬(∃x.¬Φ). If Φ is represented in the standard way as an NFA, a priori this approach results in a doubly exponential blow-up. However, the recent literature has shown that there are classes of automatic structures for which universal quantifiers can be eliminated by different means without this blow-up by treating them as first-class citizens and not resorting to double complementation. While existing lower bounds for some classes of automatic structures show that a singly exponential blow-up is unavoidable when eliminating a universal quantifier, it is not known whether there may be better approaches that avoid the naïve doubly exponential blow-up, perhaps at least in restricted settings. In this paper, we answer this question negatively and show that there is a family of NFA representing automatic relations for which the minimal NFA recognising the language after eliminating a single universal quantifier is doubly exponential, and deciding whether this language is empty is ExpSpace-complete.
Cite as

Christoph Haase and Radosław Piórkowski. Universal Quantification Makes Automatic Structures Hard to Decide. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{haase_et_al:LIPIcs.CONCUR.2023.13,
  author =	{Haase, Christoph and Pi\'{o}rkowski, Rados{\l}aw},
  title =	{{Universal Quantification Makes Automatic Structures Hard to Decide}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.13},
  URN =		{urn:nbn:de:0030-drops-190075},
  doi =		{10.4230/LIPIcs.CONCUR.2023.13},
  annote =	{Keywords: automatic structures, universal projection, state complexity, tiling problems}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2023.31
History-Deterministic Parikh Automata

Authors: Enzo Erlich, Shibashis Guha, Ismaël Jecker, Karoliina Lehtinen, and Martin Zimmermann

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract
Parikh automata extend finite automata by counters that can be tested for membership in a semilinear set, but only at the end of a run. Thereby, they preserve many of the desirable properties of finite automata. Deterministic Parikh automata are strictly weaker than nondeterministic ones, but enjoy better closure and algorithmic properties. This state of affairs motivates the study of intermediate forms of nondeterminism. Here, we investigate history-deterministic Parikh automata, i.e., automata whose nondeterminism can be resolved on the fly. This restricted form of nondeterminism is well-suited for applications which classically call for determinism, e.g., solving games and composition. We show that history-deterministic Parikh automata are strictly more expressive than deterministic ones, incomparable to unambiguous ones, and enjoy almost all of the closure properties of deterministic automata.
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Enzo Erlich, Shibashis Guha, Ismaël Jecker, Karoliina Lehtinen, and Martin Zimmermann. History-Deterministic Parikh Automata. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{erlich_et_al:LIPIcs.CONCUR.2023.31,
  author =	{Erlich, Enzo and Guha, Shibashis and Jecker, Isma\"{e}l and Lehtinen, Karoliina and Zimmermann, Martin},
  title =	{{History-Deterministic Parikh Automata}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{31:1--31:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.31},
  URN =		{urn:nbn:de:0030-drops-190250},
  doi =		{10.4230/LIPIcs.CONCUR.2023.31},
  annote =	{Keywords: Parikh automata, History-determinism, Reversal-bounded Counter Machines}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2023.36
The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets

Authors: Petr Jančar and Jérôme Leroux

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract
A set of configurations H is a home-space for a set of configurations X of a Petri net if every configuration reachable from (any configuration in) X can reach (some configuration in) H. The semilinear home-space problem for Petri nets asks, given a Petri net and semilinear sets of configurations X, H, if H is a home-space for X. In 1989, David de Frutos Escrig and Colette Johnen proved that the problem is decidable when X is a singleton and H is a finite union of linear sets with the same periods. In this paper, we show that the general (semilinear) problem is decidable. This result is obtained by proving a duality between the reachability problem and the non-home-space problem. In particular, we prove that for any Petri net and any linear set of configurations L we can effectively compute a semilinear set C of configurations, called a non-reachability core for L, such that for every set X the set L is not a home-space for X if, and only if, C is reachable from X. We show that the established relation to the reachability problem yields the Ackermann-completeness of the (semilinear) home-space problem. For this we also show that, given a Petri net with an initial marking, the set of minimal reachable markings can be constructed in Ackermannian time.
Cite as

Petr Jančar and Jérôme Leroux. The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{jancar_et_al:LIPIcs.CONCUR.2023.36,
  author =	{Jan\v{c}ar, Petr and Leroux, J\'{e}r\^{o}me},
  title =	{{The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{36:1--36:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.36},
  URN =		{urn:nbn:de:0030-drops-190300},
  doi =		{10.4230/LIPIcs.CONCUR.2023.36},
  annote =	{Keywords: Petri nets, home-space property, semilinear sets, Ackermannian complexity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.26
Rational Verification for Nash and Subgame-Perfect Equilibria in Graph Games

Authors: Léonard Brice, Jean-François Raskin, and Marie van den Bogaard

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

Abstract
We study a natural problem about rational behaviors in multiplayer non-zero-sum sequential infinite duration games played on graphs: rational verification, that consists in deciding whether all the rational answers to a given strategy satisfy some specification. We give the complexities of that problem for two major concepts of rationality: Nash equilibria and subgame-perfect equilibria, and for three major classes of payoff functions: energy, discounted-sum, and mean-payoff.
Cite as

Léonard Brice, Jean-François Raskin, and Marie van den Bogaard. Rational Verification for Nash and Subgame-Perfect Equilibria in Graph Games. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{brice_et_al:LIPIcs.MFCS.2023.26,
  author =	{Brice, L\'{e}onard and Raskin, Jean-Fran\c{c}ois and van den Bogaard, Marie},
  title =	{{Rational Verification for Nash and Subgame-Perfect Equilibria in Graph Games}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{26:1--26:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.26},
  URN =		{urn:nbn:de:0030-drops-185608},
  doi =		{10.4230/LIPIcs.MFCS.2023.26},
  annote =	{Keywords: Games on graphs, Nash equilibria, subgame-perfect equilibria}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2022.33
Pareto-Rational Verification

Authors: Véronique Bruyère, Jean-François Raskin, and Clément Tamines

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

Abstract
We study the rational verification problem which consists in verifying the correctness of a system executing in an environment that is assumed to behave rationally. We consider the model of rationality in which the environment only executes behaviors that are Pareto-optimal with regard to its set of objectives, given the behavior of the system (which is committed in advance of any interaction). We examine two ways of specifying this behavior, first by means of a deterministic Moore machine, and then by lifting its determinism. In the latter case the machine may embed several different behaviors for the system, and the universal rational verification problem aims at verifying that all of them are correct when the environment is rational. For parity objectives, we prove that the Pareto-rational verification problem is co-NP-complete and that its universal version is in PSPACE and both NP-hard and co-NP-hard. For Boolean Büchi objectives, the former problem is Π₂𝖯-complete and the latter is PSPACE-complete. We also study the case where the objectives are expressed using LTL formulas and show that the first problem is PSPACE-complete, and that the second is 2EXPTIME-complete. Both problems are also shown to be fixed-parameter tractable for parity and Boolean Büchi objectives.
Cite as

Véronique Bruyère, Jean-François Raskin, and Clément Tamines. Pareto-Rational Verification. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 33:1-33:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bruyere_et_al:LIPIcs.CONCUR.2022.33,
  author =	{Bruy\`{e}re, V\'{e}ronique and Raskin, Jean-Fran\c{c}ois and Tamines, Cl\'{e}ment},
  title =	{{Pareto-Rational Verification}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{33:1--33:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.33},
  URN =		{urn:nbn:de:0030-drops-170968},
  doi =		{10.4230/LIPIcs.CONCUR.2022.33},
  annote =	{Keywords: Rational verification, Model-checking, Pareto-optimality, \omega-regular objectives}
}
Document
DOI: 10.4230/LIPIcs.TQC.2022.11
Quantum Speedups for Treewidth

Authors: Vladislavs Kļevickis, Krišjānis Prūsis, and Jevgēnijs Vihrovs

Published in: LIPIcs, Volume 232, 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)

Abstract
In this paper, we study quantum algorithms for computing the exact value of the treewidth of a graph. Our algorithms are based on the classical algorithm by Fomin and Villanger (Combinatorica 32, 2012) that uses O(2.616ⁿ) time and polynomial space. We show three quantum algorithms with the following complexity, using QRAM in both exponential space algorithms: - O(1.618ⁿ) time and polynomial space; - O(1.554ⁿ) time and O(1.452ⁿ) space; - O(1.538ⁿ) time and space. In contrast, the fastest known classical algorithm for treewidth uses O(1.755ⁿ) time and space. The first two speed-ups are obtained in a fairly straightforward way. The first version uses additionally only Grover’s search and provides a quadratic speedup. The second speedup is more time-efficient and uses both Grover’s search and the quantum exponential dynamic programming by Ambainis et al. (SODA '19). The third version uses the specific properties of the classical algorithm and treewidth, with a modified version of the quantum dynamic programming on the hypercube. As a small side result, we give a new classical time-space tradeoff for computing treewidth in O^*(2ⁿ) time and O^*(√{2ⁿ}) space.
Cite as

Vladislavs Kļevickis, Krišjānis Prūsis, and Jevgēnijs Vihrovs. Quantum Speedups for Treewidth. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{klevickis_et_al:LIPIcs.TQC.2022.11,
  author =	{K\c{l}evickis, Vladislavs and Pr\={u}sis, Kri\v{s}j\={a}nis and Vihrovs, Jevg\={e}nijs},
  title =	{{Quantum Speedups for Treewidth}},
  booktitle =	{17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
  pages =	{11:1--11:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-237-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{232},
  editor =	{Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.11},
  URN =		{urn:nbn:de:0030-drops-165186},
  doi =		{10.4230/LIPIcs.TQC.2022.11},
  annote =	{Keywords: Quantum computation, Treewidth, Exact algorithms, Dynamic programming}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2022.115
Strategy Synthesis for Global Window PCTL

Authors: Benjamin Bordais, Damien Busatto-Gaston, Shibashis Guha, and Jean-François Raskin

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

Abstract
Given a Markov decision process (MDP) M and a formula Φ, the strategy synthesis problem asks if there exists a strategy σ s.t. the resulting Markov chain M[σ] satisfies Φ. This problem is known to be undecidable for the probabilistic temporal logic PCTL. We study a class of formulae that can be seen as a fragment of PCTL where a local, bounded horizon property is enforced all along an execution. Moreover, we allow for linear expressions in the probabilistic inequalities. This logic is at the frontier of decidability, depending on the type of strategies considered. In particular, strategy synthesis is decidable when strategies are deterministic while the general problem is undecidable.
Cite as

Benjamin Bordais, Damien Busatto-Gaston, Shibashis Guha, and Jean-François Raskin. Strategy Synthesis for Global Window PCTL. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 115:1-115:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bordais_et_al:LIPIcs.ICALP.2022.115,
  author =	{Bordais, Benjamin and Busatto-Gaston, Damien and Guha, Shibashis and Raskin, Jean-Fran\c{c}ois},
  title =	{{Strategy Synthesis for Global Window PCTL}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{115:1--115:20},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.115},
  URN =		{urn:nbn:de:0030-drops-164562},
  doi =		{10.4230/LIPIcs.ICALP.2022.115},
  annote =	{Keywords: Markov decision processes, synthesis, PCTL}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2022.116
The Complexity of SPEs in Mean-Payoff Games

Authors: Léonard Brice, Jean-François Raskin, and Marie van den Bogaard

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

Abstract
We establish that the subgame perfect equilibrium (SPE) threshold problem for mean-payoff games is NP-complete. While the SPE threshold problem was recently shown to be decidable (in doubly exponential time) and NP-hard, its exact worst case complexity was left open.
Cite as

Léonard Brice, Jean-François Raskin, and Marie van den Bogaard. The Complexity of SPEs in Mean-Payoff Games. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 116:1-116:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{brice_et_al:LIPIcs.ICALP.2022.116,
  author =	{Brice, L\'{e}onard and Raskin, Jean-Fran\c{c}ois and van den Bogaard, Marie},
  title =	{{The Complexity of SPEs in Mean-Payoff Games}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{116:1--116:20},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.116},
  URN =		{urn:nbn:de:0030-drops-164574},
  doi =		{10.4230/LIPIcs.ICALP.2022.116},
  annote =	{Keywords: Games on graphs, subgame-perfect equilibria, mean-payoff objectives}
}
Document
DOI: 10.4230/LIPIcs.CSL.2022.10
On the Complexity of SPEs in Parity Games

Authors: Léonard Brice, Jean-François Raskin, and Marie van den Bogaard

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)

Abstract
We study the complexity of problems related to subgame-perfect equilibria (SPEs) in infinite duration non zero-sum multiplayer games played on finite graphs with parity objectives. We present new complexity results that close gaps in the literature. Our techniques are based on a recent characterization of SPEs in prefix-independent games that is grounded on the notions of requirements and negotiation, and according to which the plays supported by SPEs are exactly the plays consistent with the requirement that is the least fixed point of the negotiation function. The new results are as follows. First, checking that a given requirement is a fixed point of the negotiation function is an NP-complete problem. Second, we show that the SPE constrained existence problem is NP-complete, this problem was previously known to be ExpTime-easy and NP-hard. Third, the SPE constrained existence problem is fixed-parameter tractable when the number of players and of colors are parameters. Fourth, deciding whether some requirement is the least fixed point of the negotiation function is complete for the second level of the Boolean hierarchy. Finally, the SPE-verification problem - that is, the problem of deciding whether there exists a play supported by a SPE that satisfies some LTL formula - is PSpace-complete, this problem was known to be ExpTime-easy and PSpace-hard.
Cite as

Léonard Brice, Jean-François Raskin, and Marie van den Bogaard. On the Complexity of SPEs in Parity Games. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{brice_et_al:LIPIcs.CSL.2022.10,
  author =	{Brice, L\'{e}onard and Raskin, Jean-Fran\c{c}ois and van den Bogaard, Marie},
  title =	{{On the Complexity of SPEs in Parity Games}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{10:1--10:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.10},
  URN =		{urn:nbn:de:0030-drops-157306},
  doi =		{10.4230/LIPIcs.CSL.2022.10},
  annote =	{Keywords: Games on graphs, subgame-perfect equilibria, parity objectives}
}
Document
DOI: 10.4230/LIPIcs.DISC.2021.11
Wait-Free CAS-Based Algorithms: The Burden of the Past

Authors: Denis Bédin, François Lépine, Achour Mostéfaoui, Damien Perez, and Matthieu Perrin

Published in: LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)

Abstract
Herlihy proved that CAS is universal in the classical computing system model composed of an a priori known number of processes. This means that CAS can implement, together with reads and writes, any object with a sequential specification. For this, he proposed the first universal construction capable of emulating any data structure. It has recently been proved that CAS is still universal in the infinite arrival computing model, a model where any number of processes can be created on the fly (e.g. multi-threaded systems). In this paper, we prove that CAS does not allow to implement wait-free and linearizable visible objects in the infinite model with a space complexity bounded by the number of active processes (i.e. ones that have operations in progress on this object). This paper also shows that this lower bound is tight, in the sense that this dependency can be made as low as desired (e.g. logarithmic) by proposing a wait-free and linearizable universal construction, using the compare-and-swap operation, whose space complexity in the number of ever issued operations is defined by a parameter that can be linked to any unbounded function.
Cite as

Denis Bédin, François Lépine, Achour Mostéfaoui, Damien Perez, and Matthieu Perrin. Wait-Free CAS-Based Algorithms: The Burden of the Past. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bedin_et_al:LIPIcs.DISC.2021.11,
  author =	{B\'{e}din, Denis and L\'{e}pine, Fran\c{c}ois and Most\'{e}faoui, Achour and Perez, Damien and Perrin, Matthieu},
  title =	{{Wait-Free CAS-Based Algorithms: The Burden of the Past}},
  booktitle =	{35th International Symposium on Distributed Computing (DISC 2021)},
  pages =	{11:1--11:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-210-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{209},
  editor =	{Gilbert, Seth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.11},
  URN =		{urn:nbn:de:0030-drops-148131},
  doi =		{10.4230/LIPIcs.DISC.2021.11},
  annote =	{Keywords: Compare-And-Swap, Concurrent Object, Infinite arrival model, Linearizability, Memory complexity, Multi-Threaded Systems, Shared-Memory, Universality, Wait-freedom}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2021.8
Subgame-Perfect Equilibria in Mean-Payoff Games

Authors: Léonard Brice, Jean-François Raskin, and Marie van den Bogaard

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

Abstract
In this paper, we provide an effective characterization of all the subgame-perfect equilibria in infinite duration games played on finite graphs with mean-payoff objectives. To this end, we introduce the notion of requirement, and the notion of negotiation function. We establish that the plays that are supported by SPEs are exactly those that are consistent with the least fixed point of the negotiation function. Finally, we show that the negotiation function is piecewise linear, and can be analyzed using the linear algebraic tool box. As a corollary, we prove the decidability of the SPE constrained existence problem, whose status was left open in the literature.
Cite as

Léonard Brice, Jean-François Raskin, and Marie van den Bogaard. Subgame-Perfect Equilibria in Mean-Payoff Games. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{brice_et_al:LIPIcs.CONCUR.2021.8,
  author =	{Brice, L\'{e}onard and Raskin, Jean-Fran\c{c}ois and van den Bogaard, Marie},
  title =	{{Subgame-Perfect Equilibria in Mean-Payoff Games}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.8},
  URN =		{urn:nbn:de:0030-drops-143854},
  doi =		{10.4230/LIPIcs.CONCUR.2021.8},
  annote =	{Keywords: Games on graphs, subgame-perfect equilibria, mean-payoff objectives.}
}
Document
DOI: 10.4230/LIPIcs.TQC.2021.7
Fast and Robust Quantum State Tomography from Few Basis Measurements

Authors: Daniel Stilck França, Fernando G.S L. Brandão, and Richard Kueng

Published in: LIPIcs, Volume 197, 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)

Abstract
Quantum state tomography is a powerful but resource-intensive, general solution for numerous quantum information processing tasks. This motivates the design of robust tomography procedures that use relevant resources as sparingly as possible. Important cost factors include the number of state copies and measurement settings, as well as classical postprocessing time and memory. In this work, we present and analyze an online tomography algorithm designed to optimize all the aforementioned resources at the cost of a worse dependence on accuracy. The protocol is the first to give provably optimal performance in terms of rank and dimension for state copies, measurement settings and memory. Classical runtime is also reduced substantially and numerical experiments demonstrate a favorable comparison with other state-of-the-art techniques. Further improvements are possible by executing the algorithm on a quantum computer, giving a quantum speedup for quantum state tomography.
Cite as

Daniel Stilck França, Fernando G.S L. Brandão, and Richard Kueng. Fast and Robust Quantum State Tomography from Few Basis Measurements. In 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 197, pp. 7:1-7:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{franca_et_al:LIPIcs.TQC.2021.7,
  author =	{Fran\c{c}a, Daniel Stilck and Brand\~{a}o, Fernando G.S L. and Kueng, Richard},
  title =	{{Fast and Robust Quantum State Tomography from Few Basis Measurements}},
  booktitle =	{16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)},
  pages =	{7:1--7:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-198-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{197},
  editor =	{Hsieh, Min-Hsiu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2021.7},
  URN =		{urn:nbn:de:0030-drops-140023},
  doi =		{10.4230/LIPIcs.TQC.2021.7},
  annote =	{Keywords: quantum tomography, low-rank tomography, Gibbs states, random measurements}
}
Document
DOI: 10.4230/LIPIcs.DISC.2020.24
Leaderless State-Machine Replication: Specification, Properties, Limits

Authors: Tuanir França Rezende and Pierre Sutra

Published in: LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

Abstract
Modern Internet services commonly replicate critical data across several geographical locations using state-machine replication (SMR). Due to their reliance on a leader replica, classical SMR protocols offer limited scalability and availability in this setting. To solve this problem, recent protocols follow instead a leaderless approach, in which each replica is able to make progress using a quorum of its peers. In this paper, we study this new emerging class of SMR protocols and states some of their limits. We first propose a framework that captures the essence of leaderless state-machine replication (Leaderless SMR). Then, we introduce a set of desirable properties for these protocols: (R)eliability, (O)ptimal (L)atency and (L)oad Balancing. We show that protocols matching all of the ROLL properties are subject to a trade-off between performance and reliability. We also establish a lower bound on the message delay to execute a command in protocols optimal for the ROLL properties. This lower bound explains the persistent chaining effect observed in experimental results.
Cite as

Tuanir França Rezende and Pierre Sutra. Leaderless State-Machine Replication: Specification, Properties, Limits. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{francarezende_et_al:LIPIcs.DISC.2020.24,
  author =	{Fran\c{c}a Rezende, Tuanir and Sutra, Pierre},
  title =	{{Leaderless State-Machine Replication: Specification, Properties, Limits}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{24:1--24:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-168-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{179},
  editor =	{Attiya, Hagit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.24},
  URN =		{urn:nbn:de:0030-drops-131024},
  doi =		{10.4230/LIPIcs.DISC.2020.24},
  annote =	{Keywords: Fault Tolerance, State Machine Replication, Consensus}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.53
Quantum-Inspired Classical Algorithms for Singular Value Transformation

Authors: Dhawal Jethwani, François Le Gall, and Sanjay K. Singh

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
A recent breakthrough by Tang (STOC 2019) showed how to "dequantize" the quantum algorithm for recommendation systems by Kerenidis and Prakash (ITCS 2017). The resulting algorithm, classical but "quantum-inspired", efficiently computes a low-rank approximation of the users' preference matrix. Subsequent works have shown how to construct efficient quantum-inspired algorithms for approximating the pseudo-inverse of a low-rank matrix as well, which can be used to (approximately) solve low-rank linear systems of equations. In the present paper, we pursue this line of research and develop quantum-inspired algorithms for a large class of matrix transformations that are defined via the singular value decomposition of the matrix. In particular, we obtain classical algorithms with complexity polynomially related (in most parameters) to the complexity of the best quantum algorithms for singular value transformation recently developed by Chakraborty, Gilyén and Jeffery (ICALP 2019) and Gilyén, Su, Low and Wiebe (STOC 2019).
Cite as

Dhawal Jethwani, François Le Gall, and Sanjay K. Singh. Quantum-Inspired Classical Algorithms for Singular Value Transformation. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 53:1-53:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{jethwani_et_al:LIPIcs.MFCS.2020.53,
  author =	{Jethwani, Dhawal and Le Gall, Fran\c{c}ois and Singh, Sanjay K.},
  title =	{{Quantum-Inspired Classical Algorithms for Singular Value Transformation}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{53:1--53:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.53},
  URN =		{urn:nbn:de:0030-drops-127193},
  doi =		{10.4230/LIPIcs.MFCS.2020.53},
  annote =	{Keywords: Sampling algorithms, quantum-inspired algorithms, linear algebra}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.18
Formal Proof and Analysis of an Incremental Cycle Detection Algorithm

Authors: Armaël Guéneau, Jacques-Henri Jourdan, Arthur Charguéraud, and François Pottier

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
We study a state-of-the-art incremental cycle detection algorithm due to Bender, Fineman, Gilbert, and Tarjan. We propose a simple change that allows the algorithm to be regarded as genuinely online. Then, we exploit Separation Logic with Time Credits to simultaneously verify the correctness and the worst-case amortized asymptotic complexity of the modified algorithm.
Cite as

Armaël Guéneau, Jacques-Henri Jourdan, Arthur Charguéraud, and François Pottier. Formal Proof and Analysis of an Incremental Cycle Detection Algorithm. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{gueneau_et_al:LIPIcs.ITP.2019.18,
  author =	{Gu\'{e}neau, Arma\"{e}l and Jourdan, Jacques-Henri and Chargu\'{e}raud, Arthur and Pottier, Fran\c{c}ois},
  title =	{{Formal Proof and Analysis of an Incremental Cycle Detection Algorithm}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{18:1--18:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.18},
  URN =		{urn:nbn:de:0030-drops-110739},
  doi =		{10.4230/LIPIcs.ITP.2019.18},
  annote =	{Keywords: interactive deductive program verification, complexity analysis}
}
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