Complexity Results for Checking Distributed

We consider the distributed implementability problem as: Given a labeled transition system TS together with a distribution # of its actions over a set of processes, does there exist a distributed system over # such that its global transition system is `equivalent' to TS? We consider the distributed system models of synchronous products of transition systems [Arn94] and asynchronous automata [Zie87]. In this paper we provide complexity bounds for the above problem with three interpretations of `equivalent': as transition system isomorphism, as language equivalence, and as bisimilarity. In particular, we solve problems left open in [CMT99,Mor99]. We also describe a logic programming implementation which complements the implementation for the synthesis of asynchronous automata initiated in [SEM03]