Automata For Modeling Real-Time Systems

Rajeev Alur, David L. Dill

Abstract: To model the behavior of finite-state asynchronous real-time systems we propose the notion of timed Büchi automata (TBA). TBAs are Büchi automata coupled with a mechanism to express constant bounds on the timing delays between system events. These automata accept languages of timed traces, traces in which each event has an associated real-valued time of occurrence. We show that the class of languages accepted by TBAs is closed under the operations of union, intersection and projections, and the trace language obtained by projecting the language accepted by a TBA is ω-regular. It turns out that TBAs are not closed under complement, and it is undecidable whether the language of one automaton is a subset of the language of another. This result is an obstruction to automatic verification. However, we show that a significant (proper) subclass represented by deterministic timed Muller automata (DTMA) is closed under all the boolean operations. Consequently, a system modeled by a TBA can be automatically verified with respect to a specification given as a DTMA.