4 Search Results for "Welzel, Christoph"

Document
DOI: 10.4230/LIPIcs.MFCS.2025.45
Regular Model Checking for Systems with Effectively Regular Reachability Relation

Authors: Javier Esparza and Valentin Krasotin

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Regular model checking is a well-established technique for the verification of regular transition systems (RTS): transition systems whose initial configurations and transition relation can be effectively encoded as regular languages. In 2008, To and Libkin studied RTSs in which the reachability relation (the reflexive and transitive closure of the transition relation) is also effectively regular, and showed that the recurrent reachability problem (whether a regular set L of configurations is reached infinitely often) is polynomial in the size of RTS and the transducer for the reachability relation. We extend the work of To and Libkin by studying the decidability and complexity of verifying almost-sure reachability and recurrent reachability - that is, whether L is reachable or recurrently reachable with probability 1. We then apply our results to the more common case in which only a regular overapproximation of the reachability relation is available. In particular, we extend recent complexity results on verifying safety using regular abstraction frameworks - a technique recently introduced by Czerner, the authors, and Welzel-Mohr - to liveness and almost-sure properties.
Cite as

Javier Esparza and Valentin Krasotin. Regular Model Checking for Systems with Effectively Regular Reachability Relation. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 45:1-45:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{esparza_et_al:LIPIcs.MFCS.2025.45,
  author =	{Esparza, Javier and Krasotin, Valentin},
  title =	{{Regular Model Checking for Systems with Effectively Regular Reachability Relation}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{45:1--45:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.45},
  URN =		{urn:nbn:de:0030-drops-241525},
  doi =		{10.4230/LIPIcs.MFCS.2025.45},
  annote =	{Keywords: Regular model checking, abstraction, inductive invariants}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.19
Computing Inductive Invariants of Regular Abstraction Frameworks

Authors: Philipp Czerner, Javier Esparza, Valentin Krasotin, and Christoph Welzel-Mohr

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

Abstract
Regular transition systems (RTS) are a popular formalism for modeling infinite-state systems in general, and parameterised systems in particular. In a CONCUR 22 paper, Esparza et al. introduce a novel approach to the verification of RTS, based on inductive invariants. The approach computes the intersection of all inductive invariants of a given RTS that can be expressed as CNF formulas with a bounded number of clauses, and uses it to construct an automaton recognising an overapproximation of the reachable configurations. The paper shows that the problem of deciding if the language of this automaton intersects a given regular set of unsafe configurations is in EXPSPACE and PSPACE-hard. We introduce regular abstraction frameworks, a generalisation of the approach of Esparza et al., very similar to the regular abstractions of Hong and Lin. A framework consists of a regular language of constraints, and a transducer, called the interpretation, that assigns to each constraint the set of configurations of the RTS satisfying it. Examples of regular abstraction frameworks include the formulas of Esparza et al., octagons, bounded difference matrices, and views. We show that the generalisation of the decision problem above to regular abstraction frameworks remains in EXPSPACE, and prove a matching (non-trivial) EXPSPACE-hardness bound. EXPSPACE-hardness implies that, in the worst case, the automaton recognising the overapproximation of the reachable configurations has a double-exponential number of states. We introduce a learning algorithm that computes this automaton in a lazy manner, stopping whenever the current hypothesis is already strong enough to prove safety. We report on an implementation and show that our experimental results improve on those of Esparza et al.
Cite as

Philipp Czerner, Javier Esparza, Valentin Krasotin, and Christoph Welzel-Mohr. Computing Inductive Invariants of Regular Abstraction Frameworks. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{czerner_et_al:LIPIcs.CONCUR.2024.19,
  author =	{Czerner, Philipp and Esparza, Javier and Krasotin, Valentin and Welzel-Mohr, Christoph},
  title =	{{Computing Inductive Invariants of Regular Abstraction Frameworks}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{19:1--19:18},
  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.2024.19},
  URN =		{urn:nbn:de:0030-drops-207919},
  doi =		{10.4230/LIPIcs.CONCUR.2024.19},
  annote =	{Keywords: Regular model checking, abstraction, inductive invariants}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2022.23
Regular Model Checking Upside-Down: An Invariant-Based Approach

Authors: Javier Esparza, Mikhail Raskin, and Christoph Welzel

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

Abstract
Regular model checking is a technique for the verification of infinite-state systems whose configurations can be represented as finite words over a suitable alphabet. It applies to systems whose set of initial configurations is regular, and whose transition relation is captured by a length-preserving transducer. To verify safety properties, regular model checking iteratively computes automata recognizing increasingly larger regular sets of reachable configurations, and checks if they contain unsafe configurations. Since this procedure often does not terminate, acceleration, abstraction, and widening techniques have been developed to compute a regular superset of the reachable configurations. In this paper we develop a complementary procedure. Instead of approaching the set of reachable configurations from below, we start with the set of all configurations and approach it from above. We use that the set of reachable configurations is equal to the intersection of all inductive invariants of the system. Since this intersection is non-regular in general, we introduce b-bounded invariants, defined as those representable by CNF-formulas with at most b clauses. We prove that, for every b ≥ 0, the intersection of all b-bounded inductive invariants is regular, and we construct an automaton recognizing it. We show that whether this automaton accepts some unsafe configuration is in EXPSPACE for every b ≥ 0, and PSPACE-complete for b = 1. Finally, we study how large must b be to prove safety properties of a number of benchmarks.
Cite as

Javier Esparza, Mikhail Raskin, and Christoph Welzel. Regular Model Checking Upside-Down: An Invariant-Based Approach. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 23:1-23:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{esparza_et_al:LIPIcs.CONCUR.2022.23,
  author =	{Esparza, Javier and Raskin, Mikhail and Welzel, Christoph},
  title =	{{Regular Model Checking Upside-Down: An Invariant-Based Approach}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{23:1--23:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.23},
  URN =		{urn:nbn:de:0030-drops-170862},
  doi =		{10.4230/LIPIcs.CONCUR.2022.23},
  annote =	{Keywords: parameterized verification, structural analysis, regular languages, regular model-checking, traps}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2020.37
Parameterized Complexity of Safety of Threshold Automata

Authors: A. R. Balasubramanian

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

Abstract
Threshold automata are a formalism for modeling fault-tolerant distributed algorithms. In this paper, we study the parameterized complexity of reachability of threshold automata. As a first result, we show that the problem becomes W[1]-hard even when parameterized by parameters which are quite small in practice. We then consider two restricted cases which arise in practice and provide fixed-parameter tractable algorithms for both these cases. Finally, we report on experimental results conducted on some protocols taken from the literature.
Cite as

A. R. Balasubramanian. Parameterized Complexity of Safety of Threshold Automata. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{balasubramanian:LIPIcs.FSTTCS.2020.37,
  author =	{Balasubramanian, A. R.},
  title =	{{Parameterized Complexity of Safety of Threshold Automata}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.37},
  URN =		{urn:nbn:de:0030-drops-132787},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.37},
  annote =	{Keywords: Threshold automata, distributed algorithms, parameterized complexity}
}
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