Time-Abstracting Bisimulation for Probabilistic Timed Automata

This paper focuses on probabilistic timed automata (PTA), an extension of timed automata with discrete probabilistic branchings. As the regions of these automata often lead to an exponential blowup, reduction techniques are of utmost importance. In this paper, we investigate probabilistic time-abstracting bisimulation (PTaB), an equivalence notion that abstracts from exact time delays. PTaB is proven to preserve probabilistic computational tree logic (PCTL). The region equivalence is a (very refined) PTaB. Furthermore, we provide a non-trivial adaptation of the traditional partition-refinement algorithm to compute the quotient under PTaB. This algorithm is symbolic in the sense that equivalence classes are represented as polyhedra.