A Uniform Approach for Proving the Polynomial Time Decidability of Simulation Relations for Finite State Processes

We present a uniform approach for proving the polynomial time decidability of various simulation and equivalence relations for nite state processes. Our approach applies directly to a number of simulation relations and equivalences considered in the literature including strong bisimulation Par81, Mil80, KS90], simulation equivalence vG90, HT94], ready-simulation equivalence vG90, HT94], complete simulation equivalence vG90], possibilities equivalence (also known as forward simulation) and backward simulation equivalence LV91]. The rst four relations have been shown to be polynomial time decidable using diierent techniques KS90, HT94]. The complexities of the last two equivalences have not been studied in the literature. Our approach uses eecient reductions to the satissability problem for Horn formulas. As a corollary we show that for deterministic transition systems bisimulation equivalence is in NC which resolves an open problem posed in GHR95].