A Study on Team Bisimulations for BPP Nets

Decidability of Two Truly Concurrent Equivalences for Finite Bounded Petri Nets

“…We have extended Vogler's proof technique in [15], based on ordered markings, that he used to prove decidability of (strong) fully-concurrent bisimilarity for safe nets, to bounded nets by means of indexed ordered markings. The extension is flexible enough to be applicable also to other similar equivalences, such as causal-net bisimilarity [7,9]. While decidability of fully-concurrent bisimilarity for bounded nets was already proved by Montanari and Pistore [12], our result for causal-net bisimilarity is new.…”

“…Truly concurrent equivalences, such as fully-concurrent bisimilarity [2] or causal-net bisimilarity [7,9], have been advocated as very suitable equivalences to compare the behavior of Petri nets. However, most results about their decidability [15,11,16] are limited to the class of finite safe nets, i.e., nets whose places can hold one token at most.…”

“…The third contribution of the paper is to show that our generalization of Vogler's proof technique can be adapted to prove the decidability also of another truly concurrent behavioral equivalence, namely causal-net bisimilarity [9], a behavioral equivalence that coincides with structure-preserving bisimilarity [7], and which is slightly finer than (strong) fully-concurrent bisimilarity.…”

Place Bisimilarity is Decidable, Indeed!

“…On the subclass of BPP nets (i.e., nets whose transitions have singleton pre-set), place bisimilarity coincides with team bisimilarity [10], which is actually coinductive and, for this reason, very efficiently decidable (precisely in O(m • n • log(n + 1)) time, where n is the number of places and m of transitions), characterized by a simple modal logic, and even axiomatizable over the process algebra BPP with guarded summation and guarded recursion [9]. Moreover, d-place bisimilarity specializes to h-team bisimilarity [11], which coincides with fully-concurrent bisimilarity on this subclass of P/T nets.…”

“…Essentially, a d-place bisimulation is a relation on the set whose elements are the places and the empty marking, which is considered as an additional dummy place. This weaker variant is still finer than fully-concurrent bisimilarity [3], even if on BPP nets, i.e., nets whose transitions have pre-set of size one, d-place bisimilarity specializes to h-team bisimilarity [11], which coincides with fullyconcurrent bisimilarity [3] on this class of nets.…”