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Model-Checking Parametric Lock-Sharing Systems Against Regular Constraints

Authors Corto Mascle, Anca Muscholl, Igor Walukiewicz

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Author Details

Corto Mascle
  • Université de Bordeaux, France
Anca Muscholl
  • Université de Bordeaux, France
Igor Walukiewicz
  • Université de Bordeaux, CNRS, France

Funding

Work supported by the ANR project PaVeDys.

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Corto Mascle, Anca Muscholl, and Igor Walukiewicz. Model-Checking Parametric Lock-Sharing Systems Against Regular Constraints. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CONCUR.2023.24

Abstract

In parametric lock-sharing systems processes can spawn new processes to run in parallel, and can create new locks. The behavior of every process is given by a pushdown automaton. We consider infinite behaviors of such systems under strong process fairness condition. A result of a potentially infinite execution of a system is a limit configuration, that is a potentially infinite tree. The verification problem is to determine if a given system has a limit configuration satisfying a given regular property. This formulation of the problem encompasses verification of reachability as well as of many liveness properties. We show that this verification problem, while undecidable in general, is decidable for nested lock usage.
We show Exptime-completeness of the verification problem. The main source of complexity is the number of parameters in the spawn operation. If the number of parameters is bounded, our algorithm works in Ptime for properties expressed by parity automata with a fixed number of ranks.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
Keywords
  • Parametric systems
  • Locks
  • Model-checking

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