On distributed bisimilarity over Basic Parallel Processes 1

Distributed bisimilarity is one of non-interleaving equivalences studied on concurrent systems; it refines the classical bisimilarity by taking also the spatial distribution of (sub)components into account. In the area of verification of infinite-state systems, one of the simplest (most basic) classes is the class of Basic Parallel Processes (BPP); here distributed bisimilarity is known to coincide with many other non-interleaving equivalences. While the classical (interleaving) bisimilarity on BPP is known to be PSPACE-complete, for distributed bisimilarity a polynomial time algorithm was shown by Lasota (2003). Lasota’s algorithm is technically a bit complicated, and uses the algorithm by Hirshfeld, Jerrum, Moller (1996) for deciding bisimilarity on normed BPP as a subroutine. Lasota has not estimated the degree of the polynomial for his algorithm, and it is not an easy task to do. In this paper we show a direct and conceptually simpler algorithm, which allows to bound the complexity by O(n3) (when starting from the normal form used by Lasota).