25 Search Results for "Jecker, Ismaël"

Document
DOI: 10.4230/LIPIcs.CONCUR.2024.12
History-Determinism vs Fair Simulation

Authors: Udi Boker, Thomas A. Henzinger, Karoliina Lehtinen, and Aditya Prakash

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
An automaton 𝒜 is history-deterministic if its nondeterminism can be resolved on the fly, only using the prefix of the word read so far. This mild form of nondeterminism has attracted particular attention for its applications in synthesis problems. An automaton 𝒜 is guidable with respect to a class C of automata if it can fairly simulate every automaton in C, whose language is contained in that of 𝒜. In other words, guidable automata are those for which inclusion and simulation coincide, making them particularly interesting for model-checking. We study the connection between these two notions, and specifically the question of when they coincide. For classes of automata on which they do, deciding guidability, an otherwise challenging decision problem, reduces to deciding history-determinism, a problem that is starting to be well-understood for many classes. We provide a selection of sufficient criteria for a class of automata to guarantee the coincidence of the notions, and use them to show that the notions coincide for the most common automata classes, among which are ω-regular automata and many infinite-state automata with safety and reachability acceptance conditions, including vector addition systems with states, one-counter nets, pushdown-, Parikh-, and timed-automata. We also demonstrate that history-determinism and guidability do not always coincide, for example, for the classes of timed automata with a fixed number of clocks.
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Udi Boker, Thomas A. Henzinger, Karoliina Lehtinen, and Aditya Prakash. History-Determinism vs Fair Simulation. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{boker_et_al:LIPIcs.CONCUR.2024.12,
  author =	{Boker, Udi and Henzinger, Thomas A. and Lehtinen, Karoliina and Prakash, Aditya},
  title =	{{History-Determinism vs Fair Simulation}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.12},
  URN =		{urn:nbn:de:0030-drops-207841},
  doi =		{10.4230/LIPIcs.CONCUR.2024.12},
  annote =	{Keywords: History-Determinism}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.21
Reversible Transducers over Infinite Words

Authors: Luc Dartois, Paul Gastin, Loïc Germerie Guizouarn, R. Govind, and Shankaranarayanan Krishna

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
Deterministic two-way transducers capture the class of regular functions. The efficiency of composing two-way transducers has a direct implication in algorithmic problems related to synthesis, where transformation specifications are converted into equivalent transducers. These specifications are presented in a modular way, and composing the resultant machines simulates the full specification. An important result by Dartois et al. [Luc Dartois et al., 2017] shows that composition of two-way transducers enjoy a polynomial composition when the underlying transducer is reversible, that is, if they are both deterministic and co-deterministic. This is a major improvement over general deterministic two-way transducers, for which composition causes a doubly exponential blow-up in the size of the inputs in general. Moreover, they show that reversible two-way transducers have the same expressiveness as deterministic two-way transducers. However, the notion of reversible two-way transducers over infinite words as well as the question of their expressiveness were not studied yet. In this article, we introduce the class of reversible two-way transducers over infinite words and show that they enjoy the same expressive power as deterministic two-way transducers over infinite words. This is done through a non-trivial, effective construction inducing a single exponential blow-up in the set of states. Further, we also prove that composing two reversible two-way transducers over infinite words incurs only a polynomial complexity, thereby providing an efficient procedure for composition of transducers over infinite words.
Cite as

Luc Dartois, Paul Gastin, Loïc Germerie Guizouarn, R. Govind, and Shankaranarayanan Krishna. Reversible Transducers over Infinite Words. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dartois_et_al:LIPIcs.CONCUR.2024.21,
  author =	{Dartois, Luc and Gastin, Paul and Germerie Guizouarn, Lo\"{i}c and Govind, R. and Krishna, Shankaranarayanan},
  title =	{{Reversible Transducers over Infinite Words}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{21:1--21:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.21},
  URN =		{urn:nbn:de:0030-drops-207932},
  doi =		{10.4230/LIPIcs.CONCUR.2024.21},
  annote =	{Keywords: Transducers, Regular functions, Reversibility, Composition, SSTs}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.29
Strategic Dominance: A New Preorder for Nondeterministic Processes

Authors: Thomas A. Henzinger, Nicolas Mazzocchi, and N. Ege Saraç

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We study the following refinement relation between nondeterministic state-transition models: model ℬ strategically dominates model 𝒜 iff every deterministic refinement of 𝒜 is language contained in some deterministic refinement of ℬ. While language containment is trace inclusion, and the (fair) simulation preorder coincides with tree inclusion, strategic dominance falls strictly between the two and can be characterized as "strategy inclusion" between 𝒜 and ℬ: every strategy that resolves the nondeterminism of 𝒜 is dominated by a strategy that resolves the nondeterminism of ℬ. Strategic dominance can be checked in 2-ExpTime by a decidable first-order Presburger logic with quantification over words and strategies, called resolver logic. We give several other applications of resolver logic, including checking the co-safety, co-liveness, and history-determinism of boolean and quantitative automata, and checking the inclusion between hyperproperties that are specified by nondeterministic boolean and quantitative automata.
Cite as

Thomas A. Henzinger, Nicolas Mazzocchi, and N. Ege Saraç. Strategic Dominance: A New Preorder for Nondeterministic Processes. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{henzinger_et_al:LIPIcs.CONCUR.2024.29,
  author =	{Henzinger, Thomas A. and Mazzocchi, Nicolas and Sara\c{c}, N. Ege},
  title =	{{Strategic Dominance: A New Preorder for Nondeterministic Processes}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.29},
  URN =		{urn:nbn:de:0030-drops-208011},
  doi =		{10.4230/LIPIcs.CONCUR.2024.29},
  annote =	{Keywords: quantitative automata, refinement relation, resolver, strategy, history-determinism}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.MFCS.2024.2
Challenges of the Reachability Problem in Infinite-State Systems (Invited Paper)

Authors: Wojciech Czerwiński

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
The reachability problem is a central problem for various infinite state systems like automata with pushdown, with different kinds of counters or combinations thereof. Despite its centrality and decades of research the community still lacks a lot of answers for fundamental and basic questions of that type. I briefly describe my personal viewpoint on the current state of art and emphasise interesting directions, which are worth investigating in my opinion. I also formulate several easy to formulate and understand challenges, which might be pretty hard to solve but at the same time illustrate fundamental lack of our understanding in the area.
Cite as

Wojciech Czerwiński. Challenges of the Reachability Problem in Infinite-State Systems (Invited Paper). In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 2:1-2:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{czerwinski:LIPIcs.MFCS.2024.2,
  author =	{Czerwi\'{n}ski, Wojciech},
  title =	{{Challenges of the Reachability Problem in Infinite-State Systems}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{2:1--2:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.2},
  URN =		{urn:nbn:de:0030-drops-205582},
  doi =		{10.4230/LIPIcs.MFCS.2024.2},
  annote =	{Keywords: reachability problem, infinite-state systems, vector addition systems, pushdown}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.23
Minimizing Cost Register Automata over a Field

Authors: Yahia Idriss Benalioua, Nathan Lhote, and Pierre-Alain Reynier

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
Weighted automata (WA) are an extension of finite automata that define functions from words to values in a given semiring. An alternative deterministic model, called Cost Register Automata (CRA), was introduced by Alur et al. It enriches deterministic finite automata with a finite number of registers, which store values, updated at each transition using the operations of the semiring. It is known that CRA with register updates defined by linear maps have the same expressiveness as WA. Previous works have studied the register minimization problem: given a function computable by a WA and an integer k, is it possible to realize it using a CRA with at most k registers? In this paper, we solve this problem for CRA over a field with linear register updates, using the notion of linear hull, an algebraic invariant of WA introduced recently by Bell and Smertnig. We then generalise the approach to solve a more challenging problem, that consists in minimizing simultaneously the number of states and that of registers. In addition, we also lift our results to the setting of CRA with affine updates. Last, while the linear hull was recently shown to be computable by Bell and Smertnig, no complexity bounds were given. To fill this gap, we provide two new algorithms to compute invariants of WA. This allows us to show that the register (resp. state-register) minimization problem can be solved in 2-ExpTime (resp. in NExpTime).
Cite as

Yahia Idriss Benalioua, Nathan Lhote, and Pierre-Alain Reynier. Minimizing Cost Register Automata over a Field. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{benalioua_et_al:LIPIcs.MFCS.2024.23,
  author =	{Benalioua, Yahia Idriss and Lhote, Nathan and Reynier, Pierre-Alain},
  title =	{{Minimizing Cost Register Automata over a Field}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{23:1--23:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.23},
  URN =		{urn:nbn:de:0030-drops-205798},
  doi =		{10.4230/LIPIcs.MFCS.2024.23},
  annote =	{Keywords: Weighted automata, Cost Register automata, Zariski topology}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.136
Improved Algorithm for Reachability in d-VASS

Authors: Yuxi Fu, Qizhe Yang, and Yangluo Zheng

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
An 𝖥_{d} upper bound for the reachability problem in vector addition systems with states (VASS) in fixed dimension is given, where 𝖥_d is the d-th level of the Grzegorczyk hierarchy of complexity classes. The new algorithm combines the idea of the linear path scheme characterization of the reachability in the 2-dimension VASSes with the general decomposition algorithm by Mayr, Kosaraju and Lambert. The result improves the 𝖥_{d + 4} upper bound due to Leroux and Schmitz (LICS 2019).
Cite as

Yuxi Fu, Qizhe Yang, and Yangluo Zheng. Improved Algorithm for Reachability in d-VASS. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 136:1-136:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fu_et_al:LIPIcs.ICALP.2024.136,
  author =	{Fu, Yuxi and Yang, Qizhe and Zheng, Yangluo},
  title =	{{Improved Algorithm for Reachability in d-VASS}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{136:1--136:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.136},
  URN =		{urn:nbn:de:0030-drops-202799},
  doi =		{10.4230/LIPIcs.ICALP.2024.136},
  annote =	{Keywords: Petri net, vector addition system, reachability}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2023.35
New Lower Bounds for Reachability in Vector Addition Systems

Authors: Wojciech Czerwiński, Ismaël Jecker, Sławomir Lasota, Jérôme Leroux, and Łukasz Orlikowski

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

Abstract
We investigate the dimension-parametric complexity of the reachability problem in vector addition systems with states (VASS) and its extension with pushdown stack (pushdown VASS). Up to now, the problem is known to be F_d-hard for VASS of dimension 3d+2 (the complexity class F_d corresponds to the kth level of the fast-growing hierarchy), and no essentially better bound is known for pushdown VASS. We provide a new construction that improves the lower bound for VASS: F_d-hardness in dimension 2d+3. Furthermore, building on our new insights we show a new lower bound for pushdown VASS: F_d-hardness in dimension d/2 + 6. This dimension-parametric lower bound is strictly stronger than the upper bound for VASS, which suggests that the (still unknown) complexity of the reachability problem in pushdown VASS is higher than in plain VASS (where it is Ackermann-complete).
Cite as

Wojciech Czerwiński, Ismaël Jecker, Sławomir Lasota, Jérôme Leroux, and Łukasz Orlikowski. New Lower Bounds for Reachability in Vector Addition Systems. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 35:1-35:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{czerwinski_et_al:LIPIcs.FSTTCS.2023.35,
  author =	{Czerwi\'{n}ski, Wojciech and Jecker, Isma\"{e}l and Lasota, S{\l}awomir and Leroux, J\'{e}r\^{o}me and Orlikowski, {\L}ukasz},
  title =	{{New Lower Bounds for Reachability in Vector Addition Systems}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{35:1--35:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.35},
  URN =		{urn:nbn:de:0030-drops-194088},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.35},
  annote =	{Keywords: vector addition systems, reachability problem, pushdown vector addition system, lower bounds}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2023.18
History-Deterministic Vector Addition Systems

Authors: Sougata Bose, David Purser, and Patrick Totzke

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

Abstract
We consider history-determinism, a restricted form of non-determinism, for Vector Addition Systems with States (VASS) when used as acceptors to recognise languages of finite words. History-determinism requires that the non-deterministic choices can be resolved on-the-fly; based on the past and without jeopardising acceptance of any possible continuation of the input word. Our results show that the history-deterministic (HD) VASS sit strictly between deterministic and non-deterministic VASS regardless of the number of counters. We compare the relative expressiveness of HD systems, and closure-properties of the induced language classes, with coverability and reachability semantics, and with and without ε-labelled transitions. Whereas in dimension 1, inclusion and regularity remain decidable, from dimension two onwards, HD-VASS with suitable resolver strategies, are essentially able to simulate 2-counter Minsky machines, leading to several undecidability results: It is undecidable whether a VASS is history-deterministic, or if a language equivalent history-deterministic VASS exists. Checking language inclusion between history-deterministic 2-VASS is also undecidable.
Cite as

Sougata Bose, David Purser, and Patrick Totzke. History-Deterministic Vector Addition Systems. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bose_et_al:LIPIcs.CONCUR.2023.18,
  author =	{Bose, Sougata and Purser, David and Totzke, Patrick},
  title =	{{History-Deterministic Vector Addition Systems}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{18:1--18:17},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.18},
  URN =		{urn:nbn:de:0030-drops-190120},
  doi =		{10.4230/LIPIcs.CONCUR.2023.18},
  annote =	{Keywords: Vector Addition Systems, History-determinism, Good-for Games}
}
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.
Cite as

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.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.STACS.2023.32
A Regular and Complete Notion of Delay for Streaming String Transducers

Authors: Emmanuel Filiot, Ismaël Jecker, Christof Löding, and Sarah Winter

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
The notion of delay between finite transducers is a core element of numerous fundamental results of transducer theory. The goal of this work is to provide a similar notion for more complex abstract machines: we introduce a new notion of delay tailored to measure the similarity between streaming string transducers (SST). We show that our notion is regular: we design a finite automaton that can check whether the delay between any two SSTs executions is smaller than some given bound. As a consequence, our notion enjoys good decidability properties: in particular, while equivalence between non-deterministic SSTs is undecidable, we show that equivalence up to fixed delay is decidable. Moreover, we show that our notion has good completeness properties: we prove that two SSTs are equivalent if and only if they are equivalent up to some (computable) bounded delay. Together with the regularity of our delay notion, it provides an alternative proof that SSTs equivalence is decidable. Finally, the definition of our delay notion is machine-independent, as it only depends on the origin semantics of SSTs. As a corollary, the completeness result also holds for equivalent machine models such as deterministic two-way transducers, or MSO transducers.
Cite as

Emmanuel Filiot, Ismaël Jecker, Christof Löding, and Sarah Winter. A Regular and Complete Notion of Delay for Streaming String Transducers. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{filiot_et_al:LIPIcs.STACS.2023.32,
  author =	{Filiot, Emmanuel and Jecker, Isma\"{e}l and L\"{o}ding, Christof and Winter, Sarah},
  title =	{{A Regular and Complete Notion of Delay for Streaming String Transducers}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.32},
  URN =		{urn:nbn:de:0030-drops-176843},
  doi =		{10.4230/LIPIcs.STACS.2023.32},
  annote =	{Keywords: Streaming string transducers, Delay, Origin}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2022.11
Complexity of Spatial Games

Authors: Krishnendu Chatterjee, Rasmus Ibsen-Jensen, Ismaël Jecker, and Jakub Svoboda

Published in: LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

Abstract
Spatial games form a widely-studied class of games from biology and physics modeling the evolution of social behavior. Formally, such a game is defined by a square (d by d) payoff matrix M and an undirected graph G. Each vertex of G represents an individual, that initially follows some strategy i ∈ {1,2,…,d}. In each round of the game, every individual plays the matrix game with each of its neighbors: An individual following strategy i meeting a neighbor following strategy j receives a payoff equal to the entry (i,j) of M. Then, each individual updates its strategy to its neighbors' strategy with the highest sum of payoffs, and the next round starts. The basic computational problems consist of reachability between configurations and the average frequency of a strategy. For general spatial games and graphs, these problems are in PSPACE. In this paper, we examine restricted setting: the game is a prisoner’s dilemma; and G is a subgraph of grid. We prove that basic computational problems for spatial games with prisoner’s dilemma on a subgraph of a grid are PSPACE-hard.
Cite as

Krishnendu Chatterjee, Rasmus Ibsen-Jensen, Ismaël Jecker, and Jakub Svoboda. Complexity of Spatial Games. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chatterjee_et_al:LIPIcs.FSTTCS.2022.11,
  author =	{Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Jecker, Isma\"{e}l and Svoboda, Jakub},
  title =	{{Complexity of Spatial Games}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.11},
  URN =		{urn:nbn:de:0030-drops-174038},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.11},
  annote =	{Keywords: spatial games, computational complexity, prisoner’s dilemma, dynamical systems}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2022.40
Parikh Automata over Infinite Words

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

Published in: LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

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 preserving many of the desirable algorithmic properties of finite automata. Here, we study the extension of the classical framework onto infinite inputs: We introduce reachability, safety, Büchi, and co-Büchi Parikh automata on infinite words and study expressiveness, closure properties, and the complexity of verification problems. We show that almost all classes of automata have pairwise incomparable expressiveness, both in the deterministic and the nondeterministic case; a result that sharply contrasts with the well-known hierarchy in the ω-regular setting. Furthermore, emptiness is shown decidable for Parikh automata with reachability or Büchi acceptance, but undecidable for safety and co-Büchi acceptance. Most importantly, we show decidability of model checking with specifications given by deterministic Parikh automata with safety or co-Büchi acceptance, but also undecidability for all other types of automata. Finally, solving games is undecidable for all types.
Cite as

Shibashis Guha, Ismaël Jecker, Karoliina Lehtinen, and Martin Zimmermann. Parikh Automata over Infinite Words. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 40:1-40:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{guha_et_al:LIPIcs.FSTTCS.2022.40,
  author =	{Guha, Shibashis and Jecker, Isma\"{e}l and Lehtinen, Karoliina and Zimmermann, Martin},
  title =	{{Parikh Automata over Infinite Words}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{40:1--40:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.40},
  URN =		{urn:nbn:de:0030-drops-174327},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.40},
  annote =	{Keywords: Parikh automata, \omega-automata, Infinite Games}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.MFCS.2022.3
An Updated Survey of Bidding Games on Graphs (Invited Talk)

Authors: Guy Avni and Thomas A. Henzinger

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
A graph game is a two-player zero-sum game in which the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. In bidding games, both players have budgets, and in each turn, we hold an "auction" (bidding) to determine which player moves the token. In this survey, we consider several bidding mechanisms and their effect on the properties of the game. Specifically, bidding games, and in particular bidding games of infinite duration, have an intriguing equivalence with random-turn games in which in each turn, the player who moves is chosen randomly. We summarize how minor changes in the bidding mechanism lead to unexpected differences in the equivalence with random-turn games.
Cite as

Guy Avni and Thomas A. Henzinger. An Updated Survey of Bidding Games on Graphs (Invited Talk). In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 3:1-3:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{avni_et_al:LIPIcs.MFCS.2022.3,
  author =	{Avni, Guy and Henzinger, Thomas A.},
  title =	{{An Updated Survey of Bidding Games on Graphs}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{3:1--3:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.3},
  URN =		{urn:nbn:de:0030-drops-168017},
  doi =		{10.4230/LIPIcs.MFCS.2022.3},
  annote =	{Keywords: Bidding games, Richman bidding, poorman bidding, mean-payoff, parity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.102
Algorithms and Data Structures for First-Order Logic with Connectivity Under Vertex Failures

Authors: Michał Pilipczuk, Nicole Schirrmacher, Sebastian Siebertz, Szymon Toruńczyk, and Alexandre Vigny

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

Abstract
We introduce a new data structure for answering connectivity queries in undirected graphs subject to batched vertex failures. Precisely, given any graph G and integer parameter k, we can in fixed-parameter time construct a data structure that can later be used to answer queries of the form: "are vertices s and t connected via a path that avoids vertices u₁,…, u_k?" in time 2^𝒪(k). In the terminology of the literature on data structures, this gives the first deterministic data structure for connectivity under vertex failures where for every fixed number of failures, all operations can be performed in constant time. With the aim to understand the power and the limitations of our new techniques, we prove an algorithmic meta theorem for the recently introduced separator logic, which extends first-order logic with atoms for connectivity under vertex failures. We prove that the model-checking problem for separator logic is fixed-parameter tractable on every class of graphs that exclude a fixed topological minor. We also show a weak converse. This implies that from the point of view of parameterized complexity, under standard complexity theoretical assumptions, the frontier of tractability of separator logic is almost exactly delimited by classes excluding a fixed topological minor. The backbone of our proof relies on a decomposition theorem of Cygan, Lokshtanov, Pilipczuk, Pilipczuk, and Saurabh [SICOMP '19], which provides a tree decomposition of a given graph into bags that are unbreakable. Crucially, unbreakability allows to reduce separator logic to plain first-order logic within each bag individually. Guided by this observation, we design our model-checking algorithm using dynamic programming over the tree decomposition, where the transition at each bag amounts to running a suitable model-checking subprocedure for plain first-order logic. This approach is robust enough to provide also an extension to efficient enumeration of answers to a query expressed in separator logic.
Cite as

Michał Pilipczuk, Nicole Schirrmacher, Sebastian Siebertz, Szymon Toruńczyk, and Alexandre Vigny. Algorithms and Data Structures for First-Order Logic with Connectivity Under Vertex Failures. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 102:1-102:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{pilipczuk_et_al:LIPIcs.ICALP.2022.102,
  author =	{Pilipczuk, Micha{\l} and Schirrmacher, Nicole and Siebertz, Sebastian and Toru\'{n}czyk, Szymon and Vigny, Alexandre},
  title =	{{Algorithms and Data Structures for First-Order Logic with Connectivity Under Vertex Failures}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{102:1--102:18},
  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.2022.102},
  URN =		{urn:nbn:de:0030-drops-164432},
  doi =		{10.4230/LIPIcs.ICALP.2022.102},
  annote =	{Keywords: Combinatorics and graph theory, Computational applications of logic, Data structures, Fixed-parameter algorithms and complexity, Graph algorithms}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2021.34
On the Complexity of Intersection Non-emptiness for Star-Free Language Classes

Authors: Emmanuel Arrighi, Henning Fernau, Stefan Hoffmann, Markus Holzer, Ismaël Jecker, Mateus de Oliveira Oliveira, and Petra Wolf

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
In the Intersection Non-emptiness problem, we are given a list of finite automata A_1, A_2,… , A_m over a common alphabet Σ as input, and the goal is to determine whether some string w ∈ Σ^* lies in the intersection of the languages accepted by the automata in the list. We analyze the complexity of the Intersection Non-emptiness problem under the promise that all input automata accept a language in some level of the dot-depth hierarchy, or some level of the Straubing-Thérien hierarchy. Automata accepting languages from the lowest levels of these hierarchies arise naturally in the context of model checking. We identify a dichotomy in the dot-depth hierarchy by showing that the problem is already NP-complete when all input automata accept languages of the levels B_0 or B_{1/2} and already PSPACE-hard when all automata accept a language from the level B_1. Conversely, we identify a tetrachotomy in the Straubing-Thérien hierarchy. More precisely, we show that the problem is in AC^0 when restricted to level L_0; complete for L or NL, depending on the input representation, when restricted to languages in the level L_{1/2}; NP-complete when the input is given as DFAs accepting a language in L_1 or L_{3/2}; and finally, PSPACE-complete when the input automata accept languages in level L_2 or higher. Moreover, we show that the proof technique used to show containment in NP for DFAs accepting languages in L_1 or L_{3/2} does not generalize to the context of NFAs. To prove this, we identify a family of languages that provide an exponential separation between the state complexity of general NFAs and that of partially ordered NFAs. To the best of our knowledge, this is the first superpolynomial separation between these two models of computation.
Cite as

Emmanuel Arrighi, Henning Fernau, Stefan Hoffmann, Markus Holzer, Ismaël Jecker, Mateus de Oliveira Oliveira, and Petra Wolf. On the Complexity of Intersection Non-emptiness for Star-Free Language Classes. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{arrighi_et_al:LIPIcs.FSTTCS.2021.34,
  author =	{Arrighi, Emmanuel and Fernau, Henning and Hoffmann, Stefan and Holzer, Markus and Jecker, Isma\"{e}l and de Oliveira Oliveira, Mateus and Wolf, Petra},
  title =	{{On the Complexity of Intersection Non-emptiness for Star-Free Language Classes}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.34},
  URN =		{urn:nbn:de:0030-drops-155456},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.34},
  annote =	{Keywords: Intersection Non-emptiness Problem, Star-Free Languages, Straubing-Th\'{e}rien Hierarchy, dot-depth Hierarchy, Commutative Languages, Complexity}
}
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