32 Search Results for "Zetzsche, Georg"

Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.126
Separability in Büchi VASS and Singly Non-Linear Systems of Inequalities

Authors: Pascal Baumann, Eren Keskin, Roland Meyer, and Georg Zetzsche

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

Abstract
The ω-regular separability problem for Büchi VASS coverability languages has recently been shown to be decidable, but with an EXPSPACE lower and a non-primitive recursive upper bound - the exact complexity remained open. We close this gap and show that the problem is EXPSPACE-complete. A careful analysis of our complexity bounds additionally yields a PSPACE procedure in the case of fixed dimension ≥ 1, which matches a pre-established lower bound of PSPACE for one dimensional Büchi VASS. Our algorithm is a non-deterministic search for a witness whose size, as we show, can be suitably bounded. Part of the procedure is to decide the existence of runs in VASS that satisfy certain non-linear properties. Therefore, a key technical ingredient is to analyze a class of systems of inequalities where one variable may occur in non-linear (polynomial) expressions. These so-called singly non-linear systems (SNLS) take the form A(x)⋅ y ≥ b(x), where A(x) and b(x) are a matrix resp. a vector whose entries are polynomials in x, and y ranges over vectors in the rationals. Our main contribution on SNLS is an exponential upper bound on the size of rational solutions to singly non-linear systems. The proof consists of three steps. First, we give a tailor-made quantifier elimination to characterize all real solutions to x. Second, using the root separation theorem about the distance of real roots of polynomials, we show that if a rational solution exists, then there is one with at most polynomially many bits. Third, we insert the solution for x into the SNLS, making it linear and allowing us to invoke standard solution bounds from convex geometry. Finally, we combine the results about SNLS with several techniques from the area of VASS to devise an EXPSPACE decision procedure for ω-regular separability of Büchi VASS.
Cite as

Pascal Baumann, Eren Keskin, Roland Meyer, and Georg Zetzsche. Separability in Büchi VASS and Singly Non-Linear Systems of Inequalities. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 126:1-126:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{baumann_et_al:LIPIcs.ICALP.2024.126,
  author =	{Baumann, Pascal and Keskin, Eren and Meyer, Roland and Zetzsche, Georg},
  title =	{{Separability in B\"{u}chi VASS and Singly Non-Linear Systems of Inequalities}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{126:1--126:19},
  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.2024.126},
  URN =		{urn:nbn:de:0030-drops-202695},
  doi =		{10.4230/LIPIcs.ICALP.2024.126},
  annote =	{Keywords: Vector addition systems, infinite words, separability, inequalities, quantifier elimination, rational, polynomials}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.127
Decidability of Graph Neural Networks via Logical Characterizations

Authors: Michael Benedikt, Chia-Hsuan Lu, Boris Motik, and Tony Tan

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

Abstract
We present results concerning the expressiveness and decidability of a popular graph learning formalism, graph neural networks (GNNs), exploiting connections with logic. We use a family of recently-discovered decidable logics involving "Presburger quantifiers". We show how to use these logics to measure the expressiveness of classes of GNNs, in some cases getting exact correspondences between the expressiveness of logics and GNNs. We also employ the logics, and the techniques used to analyze them, to obtain decision procedures for verification problems over GNNs. We complement this with undecidability results for static analysis problems involving the logics, as well as for GNN verification problems.
Cite as

Michael Benedikt, Chia-Hsuan Lu, Boris Motik, and Tony Tan. Decidability of Graph Neural Networks via Logical Characterizations. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 127:1-127:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{benedikt_et_al:LIPIcs.ICALP.2024.127,
  author =	{Benedikt, Michael and Lu, Chia-Hsuan and Motik, Boris and Tan, Tony},
  title =	{{Decidability of Graph Neural Networks via Logical Characterizations}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{127:1--127:20},
  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.2024.127},
  URN =		{urn:nbn:de:0030-drops-202708},
  doi =		{10.4230/LIPIcs.ICALP.2024.127},
  annote =	{Keywords: Logic, Graph Neural Networks}
}
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
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.141
Flattability of Priority Vector Addition Systems

Authors: Roland Guttenberg

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

Abstract
Vector addition systems (VAS), also known as Petri nets, are a popular model of concurrent systems. Many problems from many areas reduce to the reachability problem for VAS, which consists of deciding whether a target configuration of a VAS is reachable from a given initial configuration. One of the main approaches to solve the problem on practical instances is called flattening, intuitively removing nested loops. This technique is known to terminate for semilinear VAS due to [Jérôme Leroux, 2013]. In this paper, we prove that also for VAS with nested zero tests, called Priority VAS, flattening does in fact terminate for all semilinear reachability relations. Furthermore, we prove that Priority VAS admit semilinear inductive invariants. Both of these results are obtained by defining a well-quasi-order on runs of Priority VAS which has good pumping properties.
Cite as

Roland Guttenberg. Flattability of Priority Vector Addition Systems. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 141:1-141:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{guttenberg:LIPIcs.ICALP.2024.141,
  author =	{Guttenberg, Roland},
  title =	{{Flattability of Priority Vector Addition Systems}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{141:1--141:20},
  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.2024.141},
  URN =		{urn:nbn:de:0030-drops-202848},
  doi =		{10.4230/LIPIcs.ICALP.2024.141},
  annote =	{Keywords: Priority Vector Addition Systems, Semilinear, Inductive Invariants, Geometry, Flattability, Almost Semilinear, Transformer Relation}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.142
An Efficient Quantifier Elimination Procedure for Presburger Arithmetic

Authors: Christoph Haase, Shankara Narayanan Krishna, Khushraj Madnani, Om Swostik Mishra, and Georg Zetzsche

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

Abstract
All known quantifier elimination procedures for Presburger arithmetic require doubly exponential time for eliminating a single block of existentially quantified variables. It has even been claimed in the literature that this upper bound is tight. We observe that this claim is incorrect and develop, as the main result of this paper, a quantifier elimination procedure eliminating a block of existentially quantified variables in singly exponential time. As corollaries, we can establish the precise complexity of numerous problems. Examples include deciding (i) monadic decomposability for existential formulas, (ii) whether an existential formula defines a well-quasi ordering or, more generally, (iii) certain formulas of Presburger arithmetic with Ramsey quantifiers. Moreover, despite the exponential blowup, our procedure shows that under mild assumptions, even NP upper bounds for decision problems about quantifier-free formulas can be transferred to existential formulas. The technical basis of our results is a kind of small model property for parametric integer programming that generalizes the seminal results by von zur Gathen and Sieveking on small integer points in convex polytopes.
Cite as

Christoph Haase, Shankara Narayanan Krishna, Khushraj Madnani, Om Swostik Mishra, and Georg Zetzsche. An Efficient Quantifier Elimination Procedure for Presburger Arithmetic. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 142:1-142:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{haase_et_al:LIPIcs.ICALP.2024.142,
  author =	{Haase, Christoph and Krishna, Shankara Narayanan and Madnani, Khushraj and Mishra, Om Swostik and Zetzsche, Georg},
  title =	{{An Efficient Quantifier Elimination Procedure for Presburger Arithmetic}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{142:1--142:17},
  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.2024.142},
  URN =		{urn:nbn:de:0030-drops-202856},
  doi =		{10.4230/LIPIcs.ICALP.2024.142},
  annote =	{Keywords: Presburger arithmetic, quantifier elimination, parametric integer programming, convex geometry}
}
Document
DOI: 10.4230/LIPIcs.STACS.2024.36
Directed Regular and Context-Free Languages

Authors: Moses Ganardi, Irmak Sağlam, and Georg Zetzsche

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
We study the problem of deciding whether a given language is directed. A language L is directed if every pair of words in L have a common (scattered) superword in L. Deciding directedness is a fundamental problem in connection with ideal decompositions of downward closed sets. Another motivation is that deciding whether two directed context-free languages have the same downward closures can be decided in polynomial time, whereas for general context-free languages, this problem is known to be coNEXP-complete. We show that the directedness problem for regular languages, given as NFAs, belongs to AC¹, and thus polynomial time. Moreover, it is NL-complete for fixed alphabet sizes. Furthermore, we show that for context-free languages, the directedness problem is PSPACE-complete.
Cite as

Moses Ganardi, Irmak Sağlam, and Georg Zetzsche. Directed Regular and Context-Free Languages. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 36:1-36:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ganardi_et_al:LIPIcs.STACS.2024.36,
  author =	{Ganardi, Moses and Sa\u{g}lam, Irmak and Zetzsche, Georg},
  title =	{{Directed Regular and Context-Free Languages}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{36:1--36:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.36},
  URN =		{urn:nbn:de:0030-drops-197465},
  doi =		{10.4230/LIPIcs.STACS.2024.36},
  annote =	{Keywords: Subword, ideal, language, regular, context-free, equivalence, downward closure, compression}
}
Document
DOI: 10.4230/LIPIcs.CSL.2024.31
Remarks on Parikh-Recognizable Omega-languages

Authors: Mario Grobler, Leif Sabellek, and Sebastian Siebertz

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract
Several variants of Parikh automata on infinite words were recently introduced by Guha et al. [FSTTCS, 2022]. We show that one of these variants coincides with blind counter machine as introduced by Fernau and Stiebe [Fundamenta Informaticae, 2008]. Fernau and Stiebe showed that every ω-language recognized by a blind counter machine is of the form ⋃_iU_iV_i^ω for Parikh recognizable languages U_i, V_i, but blind counter machines fall short of characterizing this class of ω-languages. They posed as an open problem to find a suitable automata-based characterization. We introduce several additional variants of Parikh automata on infinite words that yield automata characterizations of classes of ω-language of the form ⋃_iU_iV_i^ω for all combinations of languages U_i, V_i being regular or Parikh-recognizable. When both U_i and V_i are regular, this coincides with Büchi’s classical theorem. We study the effect of ε-transitions in all variants of Parikh automata and show that almost all of them admit ε-elimination. Finally we study the classical decision problems with applications to model checking.
Cite as

Mario Grobler, Leif Sabellek, and Sebastian Siebertz. Remarks on Parikh-Recognizable Omega-languages. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 31:1-31:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{grobler_et_al:LIPIcs.CSL.2024.31,
  author =	{Grobler, Mario and Sabellek, Leif and Siebertz, Sebastian},
  title =	{{Remarks on Parikh-Recognizable Omega-languages}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{31:1--31:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello 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.CSL.2024.31},
  URN =		{urn:nbn:de:0030-drops-196743},
  doi =		{10.4230/LIPIcs.CSL.2024.31},
  annote =	{Keywords: Parikh automata, blind counter machines, infinite words, B\"{u}chi’s theorem}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2023.15
Regular Separators for VASS Coverability Languages

Authors: Chris Köcher and Georg Zetzsche

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

Abstract
We study regular separators of vector addition systems (VASS, for short) with coverability semantics. A regular language R is a regular separator of languages K and L if K ⊆ R and L ∩ R = ∅. It was shown by Czerwiński, Lasota, Meyer, Muskalla, Kumar, and Saivasan (CONCUR 2018) that it is decidable whether, for two given VASS, there exists a regular separator. In fact, they show that a regular separator exists if and only if the two VASS languages are disjoint. However, they provide a triply exponential upper bound and a doubly exponential lower bound for the size of such separators and leave open which bound is tight. We show that if two VASS have disjoint languages, then there exists a regular separator with at most doubly exponential size. Moreover, we provide tight size bounds for separators in the case of fixed dimensions and unary/binary encodings of updates and NFA/DFA separators. In particular, we settle the aforementioned question. The key ingredient in the upper bound is a structural analysis of separating automata based on the concept of basic separators, which was recently introduced by Czerwiński and the second author. This allows us to determinize (and thus complement) without the powerset construction and avoid one exponential blowup.
Cite as

Chris Köcher and Georg Zetzsche. Regular Separators for VASS Coverability Languages. 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. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kocher_et_al:LIPIcs.FSTTCS.2023.15,
  author =	{K\"{o}cher, Chris and Zetzsche, Georg},
  title =	{{Regular Separators for VASS Coverability Languages}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{15:1--15:19},
  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.2023.15},
  URN =		{urn:nbn:de:0030-drops-193883},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.15},
  annote =	{Keywords: Vector Addition System, Separability, Regular Language}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2023.42
Counter Machines with Infrequent Reversals

Authors: Alain Finkel, Shankara Narayanan Krishna, Khushraj Madnani, Rupak Majumdar, and Georg Zetzsche

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

Abstract
Bounding the number of reversals in a counter machine is one of the most prominent restrictions to achieve decidability of the reachability problem. Given this success, we explore whether this notion can be relaxed while retaining decidability. To this end, we introduce the notion of an f-reversal-bounded counter machine for a monotone function f: ℕ → ℕ. In such a machine, every run of length n makes at most f(n) reversals. Our first main result is a dichotomy theorem: We show that for every monotone function f, one of the following holds: Either (i) f grows so slowly that every f-reversal bounded counter machine is already k-reversal bounded for some constant k or (ii) f belongs to Ω(log(n)) and reachability in f-reversal bounded counter machines is undecidable. This shows that classical reversal bounding already captures the decidable cases of f-reversal bounding for any monotone function f. The key technical ingredient is an analysis of the growth of small solutions of iterated compositions of Presburger-definable constraints. In our second contribution, we investigate whether imposing f-reversal boundedness improves the complexity of the reachability problem in vector addition systems with states (VASS). Here, we obtain an analogous dichotomy: We show that either (i) f grows so slowly that every f-reversal-bounded VASS is already k-reversal-bounded for some constant k or (ii) f belongs to Ω(n) and the reachability problem for f-reversal-bounded VASS remains Ackermann-complete. This result is proven using run amalgamation in VASS. Overall, our results imply that classical restriction of reversal boundedness is a robust one.
Cite as

Alain Finkel, Shankara Narayanan Krishna, Khushraj Madnani, Rupak Majumdar, and Georg Zetzsche. Counter Machines with Infrequent Reversals. 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. 42:1-42:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{finkel_et_al:LIPIcs.FSTTCS.2023.42,
  author =	{Finkel, Alain and Krishna, Shankara Narayanan and Madnani, Khushraj and Majumdar, Rupak and Zetzsche, Georg},
  title =	{{Counter Machines with Infrequent Reversals}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{42:1--42:17},
  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.2023.42},
  URN =		{urn:nbn:de:0030-drops-194152},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.42},
  annote =	{Keywords: Counter machines, reversal-bounded, reachability, decidability, complexity}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2023.10
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
DOI: 10.4230/LIPIcs.CONCUR.2023.39
Priority Downward Closures

Authors: Ashwani Anand and Georg Zetzsche

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

Abstract
When a system sends messages through a lossy channel, then the language encoding all sequences of messages can be abstracted by its downward closure, i.e. the set of all (not necessarily contiguous) subwords. This is useful because even if the system has infinitely many states, its downward closure is a regular language. However, if the channel has congestion control based on priorities assigned to the messages, then we need a finer abstraction: The downward closure with respect to the priority embedding. As for subword-based downward closures, one can also show that these priority downward closures are always regular. While computing finite automata for the subword-based downward closure is well understood, nothing is known in the case of priorities. We initiate the study of this problem and provide algorithms to compute priority downward closures for regular languages, one-counter languages, and context-free languages.
Cite as

Ashwani Anand and Georg Zetzsche. Priority Downward Closures. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 39:1-39:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{anand_et_al:LIPIcs.CONCUR.2023.39,
  author =	{Anand, Ashwani and Zetzsche, Georg},
  title =	{{Priority Downward Closures}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{39:1--39:18},
  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.2023.39},
  URN =		{urn:nbn:de:0030-drops-190339},
  doi =		{10.4230/LIPIcs.CONCUR.2023.39},
  annote =	{Keywords: downward closure, priority order, pushdown automata, non-deterministic finite automata, abstraction, computability}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2023.3
Context-Bounded Analysis of Concurrent Programs (Invited Talk)

Authors: Pascal Baumann, Moses Ganardi, Rupak Majumdar, Ramanathan S. Thinniyam, and Georg Zetzsche

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

Abstract
Context-bounded analysis of concurrent programs is a technique to compute a sequence of under-approximations of all behaviors of the program. For a fixed bound k, a context bounded analysis considers only those runs in which a single process is interrupted at most k times. As k grows, we capture more and more behaviors of the program. Practically, context-bounding has been very effective as a bug-finding tool: many bugs can be found even with small bounds. Theoretically, context-bounded analysis is decidable for a large number of programming models for which verification problems are undecidable. In this paper, we survey some recent work in context-bounded analysis of multithreaded programs. In particular, we show a general decidability result. We study context-bounded reachability in a language-theoretic setup. We fix a class of languages (satisfying some mild conditions) from which each thread is chosen. We show context-bounded safety and termination verification problems are decidable iff emptiness is decidable for the underlying class of languages and context-bounded boundedness is decidable iff finiteness is decidable for the underlying class.
Cite as

Pascal Baumann, Moses Ganardi, Rupak Majumdar, Ramanathan S. Thinniyam, and Georg Zetzsche. Context-Bounded Analysis of Concurrent Programs (Invited Talk). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{baumann_et_al:LIPIcs.ICALP.2023.3,
  author =	{Baumann, Pascal and Ganardi, Moses and Majumdar, Rupak and Thinniyam, Ramanathan S. and Zetzsche, Georg},
  title =	{{Context-Bounded Analysis of Concurrent Programs}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{3:1--3:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.3},
  URN =		{urn:nbn:de:0030-drops-180559},
  doi =		{10.4230/LIPIcs.ICALP.2023.3},
  annote =	{Keywords: Context-bounded analysis, Multi-threaded programs, Decidability}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2023.110
Checking Refinement of Asynchronous Programs Against Context-Free Specifications

Authors: Pascal Baumann, Moses Ganardi, Rupak Majumdar, Ramanathan S. Thinniyam, and Georg Zetzsche

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

Abstract
In the language-theoretic approach to refinement verification, we check that the language of traces of an implementation all belong to the language of a specification. We consider the refinement verification problem for asynchronous programs against specifications given by a Dyck language. We show that this problem is EXPSPACE-complete - the same complexity as that of language emptiness and for refinement verification against a regular specification. Our algorithm uses several technical ingredients. First, we show that checking if the coverability language of a succinctly described vector addition system with states (VASS) is contained in a Dyck language is EXPSPACE-complete. Second, in the more technical part of the proof, we define an ordering on words and show a downward closure construction that allows replacing the (context-free) language of each task in an asynchronous program by a regular language. Unlike downward closure operations usually considered in infinite-state verification, our ordering is not a well-quasi-ordering, and we have to construct the regular language ab initio. Once the tasks can be replaced, we show a reduction to an appropriate VASS and use our first ingredient. In addition to the inherent theoretical interest, refinement verification with Dyck specifications captures common practical resource usage patterns based on reference counting, for which few algorithmic techniques were known.
Cite as

Pascal Baumann, Moses Ganardi, Rupak Majumdar, Ramanathan S. Thinniyam, and Georg Zetzsche. Checking Refinement of Asynchronous Programs Against Context-Free Specifications. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 110:1-110:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{baumann_et_al:LIPIcs.ICALP.2023.110,
  author =	{Baumann, Pascal and Ganardi, Moses and Majumdar, Rupak and Thinniyam, Ramanathan S. and Zetzsche, Georg},
  title =	{{Checking Refinement of Asynchronous Programs Against Context-Free Specifications}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{110:1--110:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.110},
  URN =		{urn:nbn:de:0030-drops-181622},
  doi =		{10.4230/LIPIcs.ICALP.2023.110},
  annote =	{Keywords: Asynchronous programs, VASS, Dyck languages, Language inclusion, Refinement verification}
}
Document
DOI: 10.4230/LIPIcs.STACS.2023.9
Regular Separability in Büchi VASS

Authors: Pascal Baumann, Roland Meyer, and Georg Zetzsche

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

Abstract
We study the (ω-)regular separability problem for Büchi VASS languages: Given two Büchi VASS with languages L₁ and L₂, check whether there is a regular language that fully contains L₁ while remaining disjoint from L₂. We show that the problem is decidable in general and PSPACE-complete in the 1-dimensional case, assuming succinct counter updates. The results rely on several arguments. We characterize the set of all regular languages disjoint from L₂. Based on this, we derive a (sound and complete) notion of inseparability witnesses, non-regular subsets of L₁. Finally, we show how to symbolically represent inseparability witnesses and how to check their existence.
Cite as

Pascal Baumann, Roland Meyer, and Georg Zetzsche. Regular Separability in Büchi VASS. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{baumann_et_al:LIPIcs.STACS.2023.9,
  author =	{Baumann, Pascal and Meyer, Roland and Zetzsche, Georg},
  title =	{{Regular Separability in B\"{u}chi VASS}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{9:1--9:19},
  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.2023.9},
  URN =		{urn:nbn:de:0030-drops-176617},
  doi =		{10.4230/LIPIcs.STACS.2023.9},
  annote =	{Keywords: Separability problem, Vector addition systems, Infinite words, Decidability}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.71
Membership Problems in Finite Groups

Authors: Markus Lohrey, Andreas Rosowski, and Georg Zetzsche

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

Abstract
We show that the subset sum problem, the knapsack problem and the rational subset membership problem for permutation groups are NP-complete. Concerning the knapsack problem we obtain NP-completeness for every fixed n ≥ 3, where n is the number of permutations in the knapsack equation. In other words: membership in products of three cyclic permutation groups is NP-complete. This sharpens a result of Luks [Eugene M. Luks, 1991], which states NP-completeness of the membership problem for products of three abelian permutation groups. We also consider the context-free membership problem in permutation groups and prove that it is PSPACE-complete but NP-complete for a restricted class of context-free grammars where acyclic derivation trees must have constant Horton-Strahler number. Our upper bounds hold for black box groups. The results for context-free membership problems in permutation groups yield new complexity bounds for various intersection non-emptiness problems for DFAs and a single context-free grammar.
Cite as

Markus Lohrey, Andreas Rosowski, and Georg Zetzsche. Membership Problems in Finite Groups. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 71:1-71:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lohrey_et_al:LIPIcs.MFCS.2022.71,
  author =	{Lohrey, Markus and Rosowski, Andreas and Zetzsche, Georg},
  title =	{{Membership Problems in Finite Groups}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{71:1--71:16},
  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.2022.71},
  URN =		{urn:nbn:de:0030-drops-168694},
  doi =		{10.4230/LIPIcs.MFCS.2022.71},
  annote =	{Keywords: algorithms for finite groups, intersection non-emptiness problems, knapsack problems in groups}
}
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