Bounded Model Checking of Incomplete Networks of Timed Automata

Abstract

Verification of real-time systems - e.g. communication protocols or embedded controllers - is an important task. One method to detect errors is called bounded model checking (BMC). In BMC the system is iteratively unfolded and then transformed into a satisfiability problem. If an appropriate solver finds the k-th instance to be satisfiable a counterexample for a given safety property has been found. In this paper we present a first approach to apply BMC to networks of timed automata (that is a system of several interacting subautomata) where parts of the network are unspecified (so called blackboxes). Here, we would like to answer the question of unrealizability, that is, is there a path of a certain length violating a safety property regardless of the implementation of the blackboxes. We provide solutions to this problem for two timed automata communication models. For the simple synchronization model, a BMC approach based on fixed transitions is introduced resulting in a SAT-Modulo-Theory formula. With respect to the use of bounded integer variables for communication, we prove unrealizability by introducing universal quantification, yielding more advanced quantified SAT-Modulo-Theory formulas.