Better abstractions for timed automata

We study the Teachability 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. (C) 2016 Elsevier Inc. All rights reserved.