We study the reachability problem for timed automata. A standard solution to this problem involves computing a search tree whose nodes are abstractions of zones. These abstractions preserve underlying simulation relations on the state space of the automaton. For both effectiveness and efficiency reasons, they are parameterized by the maximal lower and upper bounds (LU -bounds) occurring in the guards of the automaton.One such abstraction is the a LU abstraction defined by Behrmann et al. Since this abstraction can potentially yield non-convex sets, it has not been used in implementations. Firstly, we prove that a LU abstraction is the coarsest abstraction with respect to LU -bounds that is sound and complete for reachability. Secondly, we provide an efficient technique to use the a LU abstraction to solve the reachability problem.

Abstract. We consider the reachability problem for timed automata. A standard solution to this problem involves computing a search tree whose nodes are abstractions of zones. For efficiency reasons, they are parametrized by the maximal lower and upper bounds (LU -bounds) occurring in the guards of the automaton. We propose an algorithm that is updating LU -bounds during exploration of the search tree. In order to keep them as small as possible, the bounds are refined only when they enable a transition that is impossible in the unabstracted system. So our algorithm can be seen as a kind of lazy CEGAR algorithm for timed automata. We show that on several standard benchmarks, the algorithm is capable of keeping very small LU -bounds, and in consequence reduce the search space substantially.