9 Search Results for "Schmitz, Sylvain"


Document
Monus Semantics in Vector Addition Systems with States

Authors: Pascal Baumann, Khushraj Madnani, Filip Mazowiecki, and Georg Zetzsche

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


Abstract
Vector addition systems with states (VASS) are a popular model for concurrent systems. However, many decision problems have prohibitively high complexity. Therefore, it is sometimes useful to consider overapproximating semantics in which these problems can be decided more efficiently. We study an overapproximation, called monus semantics, that slightly relaxes the semantics of decrements: A key property of a vector addition systems is that in order to decrement a counter, this counter must have a positive value. In contrast, our semantics allows decrements of zero-valued counters: If such a transition is executed, the counter just remains zero. It turns out that if only a subset of transitions is used with monus semantics (and the others with classical semantics), then reachability is undecidable. However, we show that if monus semantics is used throughout, reachability remains decidable. In particular, we show that reachability for VASS with monus semantics is as hard as that of classical VASS (i.e. Ackermann-hard), while the zero-reachability and coverability are easier (i.e. EXPSPACE-complete and NP-complete, respectively). We provide a comprehensive account of the complexity of the general reachability problem, reachability of zero configurations, and coverability under monus semantics. We study these problems in general VASS, two-dimensional VASS, and one-dimensional VASS, with unary and binary counter updates.

Cite as

Pascal Baumann, Khushraj Madnani, Filip Mazowiecki, and Georg Zetzsche. Monus Semantics in Vector Addition Systems with States. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{baumann_et_al:LIPIcs.CONCUR.2023.10,
  author =	{Baumann, Pascal and Madnani, Khushraj and Mazowiecki, Filip and Zetzsche, Georg},
  title =	{{Monus Semantics in Vector Addition Systems with States}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{10:1--10:18},
  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.2023.10},
  URN =		{urn:nbn:de:0030-drops-190047},
  doi =		{10.4230/LIPIcs.CONCUR.2023.10},
  annote =	{Keywords: Vector addition systems, Overapproximation, Reachability, Coverability}
}
Document
Decision Problems for Linear Logic with Least and Greatest Fixed Points

Authors: Anupam Das, Abhishek De, and Alexis Saurin

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)


Abstract
Linear logic is an important logic for modelling resources and decomposing computational interpretations of proofs. Decision problems for fragments of linear logic exhibiting "infinitary" behaviour (such as exponentials) are notoriously complicated. In this work, we address the decision problems for variations of linear logic with fixed points (μMALL), in particular, recent systems based on "circular" and "non-wellfounded" reasoning. In this paper, we show that μMALL is undecidable. More explicitly, we show that the general non-wellfounded system is Π⁰₁-hard via a reduction to the non-halting of Minsky machines, and thus is strictly stronger than its circular counterpart (which is in Σ⁰₁). Moreover, we show that the restriction of these systems to theorems with only the least fixed points is already Σ⁰₁-complete via a reduction to the reachability problem of alternating vector addition systems with states. This implies that both the circular system and the finitary system (with explicit (co)induction) are Σ⁰₁-complete.

Cite as

Anupam Das, Abhishek De, and Alexis Saurin. Decision Problems for Linear Logic with Least and Greatest Fixed Points. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{das_et_al:LIPIcs.FSCD.2022.20,
  author =	{Das, Anupam and De, Abhishek and Saurin, Alexis},
  title =	{{Decision Problems for Linear Logic with Least and Greatest Fixed Points}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.20},
  URN =		{urn:nbn:de:0030-drops-163019},
  doi =		{10.4230/LIPIcs.FSCD.2022.20},
  annote =	{Keywords: Linear logic, fixed points, decidability, vector addition systems}
}
Document
Invited Talk
Branching in Well-Structured Transition Systems (Invited Talk)

Authors: Sylvain Schmitz

Published in: LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)


Abstract
The framework of well-structured transition systems has been highly successful in providing generic algorithms to show the decidability of verification problems for infinite-state systems. In some of these applications, the executions in the system at hand are actually trees, and need to be "lifted" to executions over sets of configurations in order to fit in the framework. The downside of this approach is that we might lose precision when analysing the computational complexity of the algorithms, compared to reasoning over branching executions.

Cite as

Sylvain Schmitz. Branching in Well-Structured Transition Systems (Invited Talk). In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 3:1-3:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{schmitz:LIPIcs.CSL.2021.3,
  author =	{Schmitz, Sylvain},
  title =	{{Branching in Well-Structured Transition Systems}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{3:1--3:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Baier, Christel and Goubault-Larrecq, Jean},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.3},
  URN =		{urn:nbn:de:0030-drops-134377},
  doi =		{10.4230/LIPIcs.CSL.2021.3},
  annote =	{Keywords: fast-growing complexity, well-structured transition system}
}
Document
Preservation Theorems Through the Lens of Topology

Authors: Aliaume Lopez

Published in: LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)


Abstract
In this paper, we introduce a family of topological spaces that captures the existence of preservation theorems. The structure of those spaces allows us to study the relativisation of preservation theorems under suitable definitions of surjective morphisms, subclasses, sums, products, topological closures, and projective limits. Throughout the paper, we also integrate already known results into this new framework and show how it captures the essence of their proofs.

Cite as

Aliaume Lopez. Preservation Theorems Through the Lens of Topology. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 32:1-32:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{lopez:LIPIcs.CSL.2021.32,
  author =	{Lopez, Aliaume},
  title =	{{Preservation Theorems Through the Lens of Topology}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{32:1--32:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Baier, Christel and Goubault-Larrecq, Jean},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.32},
  URN =		{urn:nbn:de:0030-drops-134660},
  doi =		{10.4230/LIPIcs.CSL.2021.32},
  annote =	{Keywords: Preservation theorem, Pre-spectral space, Noetherian space, Spectral space}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
The Parametric Complexity of Lossy Counter Machines (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors: Sylvain Schmitz

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)


Abstract
The reachability problem in lossy counter machines is the best-known ACKERMANN-complete problem and has been used to establish most of the ACKERMANN-hardness statements in the literature. This hides however a complexity gap when the number of counters is fixed. We close this gap and prove F_d-completeness for machines with d counters, which provides the first known uncontrived problems complete for the fast-growing complexity classes at levels 3 < d < omega. We develop for this an approach through antichain factorisations of bad sequences and analysing the length of controlled antichains.

Cite as

Sylvain Schmitz. The Parametric Complexity of Lossy Counter Machines (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 129:1-129:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{schmitz:LIPIcs.ICALP.2019.129,
  author =	{Schmitz, Sylvain},
  title =	{{The Parametric Complexity of Lossy Counter Machines}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{129:1--129:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.129},
  URN =		{urn:nbn:de:0030-drops-107056},
  doi =		{10.4230/LIPIcs.ICALP.2019.129},
  annote =	{Keywords: Counter machine, well-structured system, well-quasi-order, antichain, fast-growing complexity}
}
Document
A Hypersequent Calculus with Clusters for Tense Logic over Ordinals

Authors: David Baelde, Anthony Lick, and Sylvain Schmitz

Published in: LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)


Abstract
Prior's tense logic forms the core of linear temporal logic, with both past- and future-looking modalities. We present a sound and complete proof system for tense logic over ordinals. Technically, this is a hypersequent system, enriched with an ordering, clusters, and annotations. The system is designed with proof search algorithms in mind, and yields an optimal coNP complexity for the validity problem. It entails a small model property for tense logic over ordinals: every satisfiable formula has a model of order type at most omega^2. It also allows to answer the validity problem for ordinals below or exactly equal to a given one.

Cite as

David Baelde, Anthony Lick, and Sylvain Schmitz. A Hypersequent Calculus with Clusters for Tense Logic over Ordinals. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{baelde_et_al:LIPIcs.FSTTCS.2018.15,
  author =	{Baelde, David and Lick, Anthony and Schmitz, Sylvain},
  title =	{{A Hypersequent Calculus with Clusters for Tense Logic over Ordinals}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{15:1--15:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Ganguly, Sumit and Pandya, Paritosh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.15},
  URN =		{urn:nbn:de:0030-drops-99143},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.15},
  annote =	{Keywords: modal logic, proof system, hypersequent}
}
Document
A Sequent Calculus for a Modal Logic on Finite Data Trees

Authors: David Baelde, Simon Lunel, and Sylvain Schmitz

Published in: LIPIcs, Volume 62, 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)


Abstract
We investigate the proof theory of a modal fragment of XPath equipped with data (in)equality tests over finite data trees, i.e., over finite unranked trees where nodes are labelled with both a symbol from a finite alphabet and a single data value from an infinite domain. We present a sound and complete sequent calculus for this logic, which yields the optimal PSPACE complexity bound for its validity problem.

Cite as

David Baelde, Simon Lunel, and Sylvain Schmitz. A Sequent Calculus for a Modal Logic on Finite Data Trees. In 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 62, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{baelde_et_al:LIPIcs.CSL.2016.32,
  author =	{Baelde, David and Lunel, Simon and Schmitz, Sylvain},
  title =	{{A Sequent Calculus for a Modal Logic on Finite Data Trees}},
  booktitle =	{25th EACSL Annual Conference on Computer Science Logic (CSL 2016)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-022-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{62},
  editor =	{Talbot, Jean-Marc and Regnier, Laurent},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2016.32},
  URN =		{urn:nbn:de:0030-drops-65720},
  doi =		{10.4230/LIPIcs.CSL.2016.32},
  annote =	{Keywords: XPath, proof systems, modal logic, complexity}
}
Document
Deciding Piecewise Testable Separability for Regular Tree Languages

Authors: Jean Goubault-Larrecq and Sylvain Schmitz

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)


Abstract
The piecewise testable separability problem asks, given two input languages, whether there exists a piecewise testable language that contains the first input language and is disjoint from the second. We prove a general characterisation of piecewise testable separability on languages in a well-quasiorder, in terms of ideals of the ordering. This subsumes the known characterisations in the case of finite words. In the case of finite ranked trees ordered by homeomorphic embedding, we show using effective representations for tree ideals that it entails the decidability of piecewise testable separability when the input languages are regular. A final byproduct is a new proof of the decidability of whether an input regular language of ranked trees is piecewise testable, which was first shown in the unranked case by Bojanczyk, Segoufin, and Straubing [Log. Meth. in Comput. Sci., 8(3:26), 2012].

Cite as

Jean Goubault-Larrecq and Sylvain Schmitz. Deciding Piecewise Testable Separability for Regular Tree Languages. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 97:1-97:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{goubaultlarrecq_et_al:LIPIcs.ICALP.2016.97,
  author =	{Goubault-Larrecq, Jean and Schmitz, Sylvain},
  title =	{{Deciding Piecewise Testable Separability for Regular Tree Languages}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{97:1--97:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.97},
  URN =		{urn:nbn:de:0030-drops-62321},
  doi =		{10.4230/LIPIcs.ICALP.2016.97},
  annote =	{Keywords: Well-quasi-order, ideal, tree languages, first-order logic}
}
Document
Invited Talk
Ideal Decompositions for Vector Addition Systems (Invited Talk)

Authors: Jérôme Leroux and Sylvain Schmitz

Published in: LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)


Abstract
Vector addition systems, or equivalently Petri nets, are one of the most popular formal models for the representation and the analysis of parallel processes. Many problems for vector addition systems are known to be decidable thanks to the theory of well-structured transition systems. Indeed, vector addition systems with configurations equipped with the classical point-wise ordering are well-structured transition systems. Based on this observation, problems like coverability or termination can be proven decidable. However, the theory of well-structured transition systems does not explain the decidability of the reachability problem. In this presentation, we show that runs of vector addition systems can also be equipped with a well quasi-order. This observation provides a unified understanding of the data structures involved in solving many problems for vector addition systems, including the central reachability problem.

Cite as

Jérôme Leroux and Sylvain Schmitz. Ideal Decompositions for Vector Addition Systems (Invited Talk). In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 1:1-1:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{leroux_et_al:LIPIcs.STACS.2016.1,
  author =	{Leroux, J\'{e}r\^{o}me and Schmitz, Sylvain},
  title =	{{Ideal Decompositions for Vector Addition Systems}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{1:1--1:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Ollinger, Nicolas and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.1},
  URN =		{urn:nbn:de:0030-drops-57024},
  doi =		{10.4230/LIPIcs.STACS.2016.1},
  annote =	{Keywords: Petri net, ideal, well-quasi-order, reachability, verification}
}
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