A Study on Team Bisimulations for BPP nets

BPP nets, a subclass of finite P/T nets, were equipped in [13] with an efficiently decidable, truly concurrent, behavioral equivalence, called team bisi-milarity. This equivalence is a very intuitive extension of classic bisimulation equivalence (over labeled transition systems) to BPP nets and it is checked in a distributed manner, without building a global model of the overall behavior of the marked BPP net. This paper has three goals. First, we provide BPP nets with various causality-based equivalences, notably a novel one, called causal-net bisimilarity, and (a version of) fully-concurrent bisimilarity [3]. Then, we define a variant equivalence, h-team bisimilarity, coarser than team bisimilarity. Then, we complete the study by comparing them with the causality-based semantics we have introduced: the main results are that team bisimilarity coincides with causal-net bisimilarity, while h-team bisimilarity with fully-concurrent bisimilarity.