Using non-convex approximations for efficient analysis of timed automata: Extended version

Frédéric Herbreteau (1) , D. Kini (2) , B. Srivathsan (1) , Igor Walukiewicz (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 Department of Computer Science and Engineering [Bombay]

The reachability problem for timed automata asks if there exists a path from its initial state to a given target state. The standard solution to this problem involves computing the zone graph of the automaton, which in principle could be infinite. In order to make the graph finite, zones are approximated using an extrapolation operator. For reasons of efficiency it is required that an extrapolation of a zone is always a zone; and in particular that it is convex. In this paper, we propose to solve the reachability problem without such extrapolation operators. To ensure termination, we provide an efficient algorithm to check if a zone is included in the so called region closure of another. Although theoretically better, closure cannot be used in the standard algorithm since a closure of a zone may not be convex. The structure of this new algorithm permits to calculate approximating parameters on-the-fly during exploration of the zone graph, as opposed to the current methods which do it by a static analysis of the automaton prior to the exploration. This allows for further improvements in the algorithm. Promising experimental results are presented.

Domaines: Logique en informatique [cs.LO]

Frédéric Herbreteau, D. Kini, B. Srivathsan, Igor Walukiewicz. Using non-convex approximations for efficient analysis of timed automata: Extended version. 2011. ⟨inria-00559902v1⟩