ON A CLASS OF TIMER HYBRID SYSTEMS REDUCIBLE TO FINITE-STATE AUTOMATA

A hybrid timer system with different timer rates and idling timer feature operating in dense time is modeled as an event-driven nondeterministic automaton and it is shown that the system is weak bisimulation equivalent to a finite state nondeterministic automaton. Our original model is an event driven infinite state automaton as in Dill (1989) and an explicit representation for the bisimulation equivalent finite state automaton whose state set consists of an index set of active timers and n pairs of bounded nonnegative integers or the symbol +infinity is derived where n is the number of clocks. The reduced model is simpler than Dill's difference bound matrix model-and similar to the model used in Alur et al. (1990)-for the finite system automaton since all difference inequalities are represented by a single order vector of integers.