The polynomial time decidability of simulation relations for finite processes: A HORNSAT based approach

Abstract

We present a uniform approach for proving the polynomial time decidability of various simulation and equivalence relations for-nite state processes. Our approach involves eecient reductions to the satissability problem for Horn formulas. It applies directly and naturally to most of the simulation preorders and equivalence relations, studied in the literature. Here we illustrate our methodology by deriving eecient algorithms for a number of such relations. For some of these relations, we present polynomial time algorithms for the rst time in the literature. We also present a HORNSAT based interpretation of the existing bottom-up algorithm for bisimulation equivalence KS90] to provide a better understanding of such bottom-up partition based methods KS90, PT87]. Corollaries of our results include an NC algorithm for bisimulation equivalence for deterministic transition system (posed as an open problem in GHR95]), an easy algorithm for computing simulations on nite graphs HHK95] etc. Our approach naturally gives rise to algorithms which are on the y VW86, FM91], local CS91, Lar92] and incremental SS94]. Moreover , diagnostic information CC92, FM91] can be obtained without any additional complexity overhead in this methodology.