Timed Automata Verification using Interpolants

The behavior of safety critical systems is often constrained by real time requirements. To model time dependent behavior and enable formal verification, timed automata are widely used as a formal model of such systems. However, due to real-valued clock variables, the state space of these systems is not finite, thus model checkers for timed automata are usually based on zone abstraction. The coarseness of the abstraction profoundly impacts performance of the analysis. In this paper, we propose a lazy abstraction algorithm based on interpolation for zones to enable efficient reachability checking for timed automata. In order to efficiently handle zone abstraction, we define interpolation in terms of difference bound matrices. We extend the notion of zone interpolants to sequences of transitions of a timed automaton, thus enabling the use of zone interpolants for abstraction refinement.