A partial order semantics approach to the clock explosion problem of timed automata

We present a new approach to the symbolic model checking of timed automata based on a partial order semantics. It relies on event zones that use vectors of event occurrences instead of clock zones that use vectors of clock values grouped in polyhedral clock constraints. We provide a description of the different congruences that arise when we consider an independence relation in a timed framework. We introduce a new abstraction, called catchup equivalence which is defined on event zones and which can be seen as an implementation of one of the (more abstract) previous congruences. This formal language approach helps clarifying what the issues are and which properties abstractions should have. The catchup equivalence yields an algorithm to check emptiness which has the same complexity bound in the worst case as the algorithm to test emptiness in the classical semantics of timed automata. Our approach works for the class of timed automata proposed by Alur-Dill, except for state invariants (an extension including state invariants is discussed informally). First experiments show that the approach is promising and may yield very significant improvements.

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