A study on team bisimulation and H-team bisimulation for BPP nets

A subclass of finite Petri nets, called BPP nets (acronym of Basic Parallel Processes), was recently equipped with an efficiently decidable, truly concurrent, bisimulation-based, behavioral equivalence, called team bisimilarity. 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. This paper has three goals. First of all, we provide BPP nets with various causality-based observational semantics, notably a novel semantics, called causal-net bisimilarity. Then, we define a variant semantics, called h-team bisimilarity, coarser than team bisimilarity, for which we adapt the modal logic characterization and the axiomatization of team bisimilarity. Then, we complete the study about team bisimilarity and h-team bisimilarity, 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.