2 Search Results for "Welzel, Christoph"

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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