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

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

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

International audienceThe reachability problem for timed automata asks if a given automaton has a run leading to an accepting state, and the liveness problem asks if the automaton has an infinite run which visits accepting states infinitely often. Both these problems are known to be Pspace-complete. We show that if P Pspace, the liveness problem is more difficult than the reachability problem; in other words 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 Pspace-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 existing solutions. CCS Concepts: • Theory of computation → Verification by model checking

Computer Aided Verification

This open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency