Discrete Bounded Bisimulation on Hybrid Automata
نویسندگان
چکیده
Hybrid automata are the prevailing formalisms to reason about systems that consist of discrete and continuous functions. Several specializations like o-minimal hybrid automata have been considered that should (1) retain as much expressibility as possible, and (2) lead to decidable (reachability) problems. However, the discrete transitions of o-minimal automata require constant resets of the continuous variables, which limits their applicability. In this paper, we consider fully o-minimal hybrid automata that employ general o-minimal functions as resets for their discrete transitions. We introduce the general abstraction tool of discrete bounded bisimulation that (1) approximates bisimulation (2) is proved to have a finite quotient on fully o-minimal hybrid automata. We show that discrete bounded bisimulation can be used as the fundation of a dynamic partition refinement algorithm for bounded reachability on (fully o-minimal) hybrid automata. The results of this paper are therefore the foundation for bounded model checking of fully o-minimal hybrid automata.
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