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Why Liveness for Timed Automata Is Hard, and What We Can Do About It

Authors Frédéric Herbreteau, B. Srivathsan, Thanh-Tung Tran, Igor Walukiewicz

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Frédéric Herbreteau
B. Srivathsan
Thanh-Tung Tran
Igor Walukiewicz

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Frédéric Herbreteau, B. Srivathsan, Thanh-Tung Tran, and Igor Walukiewicz. Why Liveness for Timed Automata Is Hard, and What We Can Do About It. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 48:1-48:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.FSTTCS.2016.48

Abstract

The liveness problem for timed automata asks if a given automaton has a run passing infinitely often through an accepting state. We show that unless P=NP, the liveness problem is more difficult than the reachability problem; more precisely, we exhibit a family of automata for which solving the reachability problem with the standard algorithm is in P but solving the liveness problem is NP-hard. This leads us to revisit the algorithmics for the liveness problem. We propose a notion of a witness for the fact that a timed automaton violates a liveness property. We give an algorithm for computing such a witness and compare it with the existing solutions.

Subject Classification

Keywords
  • Timed automata
  • model-checking
  • liveness invariant
  • state subsumption

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