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Reachability in Timed Automata with Diagonal Constraints

Authors Paul Gastin, Sayan Mukherjee, B. Srivathsan

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ACM Subject Classification
  • Theory of computation → Verification by model checking
Keywords
  • Timed Automata
  • Reachability
  • Zones
  • Diagonal constraints

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Abstract

We consider the reachability problem for timed automata having diagonal constraints (like x - y < 5) as guards in transitions. The best algorithms for timed automata proceed by enumerating reachable sets of its configurations, stored in a data structure called "zones". Simulation relations between zones are essential to ensure termination and efficiency. The algorithm employs a simulation test Z <= Z' which ascertains that zone Z does not reach more states than zone Z', and hence further enumeration from Z is not necessary. No effective simulations are known for timed automata containing diagonal constraints as guards. We propose a simulation relation <=_{LU}^d for timed automata with diagonal constraints. On the negative side, we show that deciding Z not <=_{LU}^d Z' is NP-complete. On the positive side, we identify a witness for Z not <=_{LU}^d Z' and propose an algorithm to decide the existence of such a witness using an SMT solver. The shape of the witness reveals that the simulation test is likely to be efficient in practice.

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Paul Gastin, Sayan Mukherjee, and B. Srivathsan. Reachability in Timed Automata with Diagonal Constraints. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 28:1-28:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.CONCUR.2018.28

Author Details

Paul Gastin
  • LSV, CNRS, ENS Paris-Saclay, Université Paris - Saclay, France
Sayan Mukherjee
  • Chennai Mathematical Institute, India
B. Srivathsan
  • Chennai Mathematical Institute, India

Funding

Partly supported by UMI RELAX, Infosys foundation (India) and Tata Consultancy Services - Innovation Labs (Pune, India)

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