Why Liveness for Timed Automata Is Hard, and What We Can Do About It
Frédéric Herbreteau, B. Srivathsan, Thanh-Tung Tran, Igor Walukiewicz · ACM Transactions on Computational Logic · 2020
The 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 that visits accepting states infinitely often. Both of these problems are known to be P space -complete. We show that if P ≠P space , 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 P space -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 to existing solutions.