Non-interleaving bisimulation equivalences on Basic Parallel Processes

We show polynomial time algorithms for deciding hereditary history preserving bisimilarity (in O ( n 3 log n ) ) and history preserving bisimilarity (in O ( n 6 ) ) on the class Basic Parallel Processes. The latter algorithm also decides a number of other non-interleaving behavioural equivalences (e. g. , distributed bisimilarity) which are known to coincide with history preserving bisimilarity on this class. The common general scheme of both algorithms is based on a fixpoint characterization of the equivalences for tree-like labelled event structures. The technique for realizing the greatest fixpoint computation in the case of hereditary history preserving bisimilarity is based on the revealed tight relationship between equivalent tree-like labelled event structures. In the case of history preserving bisimilarity, a technique of deciding classical bisimilarity on acyclic Petri nets is used.

Authors

• Sibylle Fröschle
• Petr Jančar
• Slawomir Lasota
• Zdeněk Sawa

Keywords

• Verification
• Equivalence checking
• Non-interleaving equivalences
• Labelled event structures
• Hereditary history preserving bisimilarity
• History preserving bisimilarity
• Bisimulation equivalence
• Basic Parallel processes