The Power of Hybrid Acceleration
This paper addresses the problem of computing symbolically the set of reachable configurations of a linear hybrid automaton. A solution proposed in earlier work consists in exploring the reachable configurations using an acceleration operator for computing the iterated effect of selected control cycles. Unfortunately, this method imposes a periodicity requirement on the data transformations labeling these cycles, that is not always satisfied in practice. This happens in particular with the important subclass of timed automata, even though it is known that the paths of such automata have a periodic behavior.
The goal of this paper is to broaden substantially the applicability of hybrid acceleration. This is done by introducing powerful reduction rules, aimed at translating hybrid data transformations into equivalent ones that satisfy the periodicity criterion. In particular, we show that these rules always succeed in the case of timed automata. This makes it possible to compute an exact symbolic representation of the set of reachable configurations of a linear hybrid automaton, with a guarantee of termination over the subclass of timed automata. Compared to other known solutions to this problem, our method is simpler, and applicable to a much larger class of systems.
KeywordsReduction Rule Simple Loop Hybrid Automaton Time Automaton Linear Hybrid
Unable to display preview. Download preview PDF.
- [BBR97]Boigelot, B., Bronne, L., Rassart, S.: An improved reachability analysis method for strongly linear hybrid systems. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 167–177. Springer, Heidelberg (1997)Google Scholar
- [Boi98]Boigelot, B.: Symbolic Methods for Exploring Infinite State Spaces. PhD thesis, Université de Liège (1998)Google Scholar
- [Fri98]Fribourg, L.: A closed-form evaluation for extended timed automata. Research Report LSV-98-2, LSV (March 1998)Google Scholar
- [LASH]The Liège Automata-based Symbolic Handler (LASH), Available at: http://www.montefiore.ulg.ac.be/~boigelot/research/lash/
- [Wei99]Weispfenning, V.: Mixed real-integer linear quantifier elimination. In: ISSAC: Proceedings of the ACM SIGSAM Int. Symp. on Symbolic and Algebraic Computation, Vancouver, pp. 129–136. ACM Press, New York (1999)Google Scholar