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.
Abstract. Standard algorithms for reachability analysis of timed automata are sensitive to the order in which the transitions of the automata are taken. To tackle this problem, we propose a ranking system and a waiting strategy. This paper discusses the reason why the search order matters and shows how a ranking system and a waiting strategy can be integrated into the standard reachability algorithm to alleviate and prevent the problem respectively. Experiments show that the combination of the two approaches gives optimal search order on standard benchmarks except for one example. This suggests that it should be used instead of the standard BFS algorithm for reachability analysis of timed automata.
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