On the Complexity of Bisimulation Problems for Basic Parallel Processes

Strong bisimilarity of Basic Parallel Processes (BPP) is decidable, but the best known algorithm has non-elementary complexity [7]. On the other hand, no lower bound for the problem was known. We show that strong bisimilarity of BPP is co-NP-hard. Weak bisimilarity of BPP is not known to be decidable, but an NP lower bound has been shown in [31]. We improve this result by showing that weak bisimilarity of BPP is \Pi p 2 -hard. Finally, we show that the problems if a BPP is regular (i.e., finite) w.r.t. strong and weak bisimilarity are co-NP-hard and \Pi p 2 -hard, respectively