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Checking Timed Büchi Automata Emptiness Using the Local-Time Semantics

Authors Frédéric Herbreteau , B. Srivathsan , Igor Walukiewicz



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Author Details

Frédéric Herbreteau
  • Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, F-33400, Talence, France
B. Srivathsan
  • Chennai Mathematical Institute, India
  • CNRS IRL 2000, ReLaX, Chennai, India
Igor Walukiewicz
  • Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, F-33400, Talence, France

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Frédéric Herbreteau, B. Srivathsan, and Igor Walukiewicz. Checking Timed Büchi Automata Emptiness Using the Local-Time Semantics. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 12:1-12:24, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.CONCUR.2022.12

Abstract

We study the Büchi non-emptiness problem for networks of timed automata. Standard solutions consider the network as a monolithic timed automaton obtained as a synchronized product and build its zone graph on-the-fly under the classical global-time semantics. In the global-time semantics, all processes are assumed to have a common global timeline. Bengtsson et al. in 1998 have proposed a local-time semantics where each process in the network moves independently according to a local timeline, and processes synchronize their timelines when they do a common action. It has been shown that the local-time semantics is equivalent to the global-time semantics for finite runs, and hence can be used for checking reachability. The local-time semantics allows computation of a local zone graph which has good independence properties and is amenable to partial-order methods. Hence local zone graphs are able to better tackle the state-space explosion due to concurrency. In this work, we extend the results to the Büchi setting. We propose a local zone graph computation that can be coupled with a partial-order method, to solve the Büchi non-emptiness problem in timed networks. In the process, we develop a theory of regions for the local-time semantics.

Subject Classification

ACM Subject Classification
  • Theory of computation → Verification by model checking
Keywords
  • Timed Büchi automata
  • local-time semantics
  • zones
  • abstraction
  • partial-order reduction

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