Fröschle, Sibylle B.Sibylle B.FröschleJančar, PetrPetrJančarLasota, SławomirSławomirLasotaSawa, ZdeněkZdeněkSawa2021-12-142021-12-142009-06-21Information and Computation 208 (1): 42-62 (2010)http://hdl.handle.net/11420/11282We show polynomial time algorithms for deciding hereditary history preserving bisimilarity (in O (n3 log n)) and history preserving bisimilarity (in O (n6)) 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.en1090-2651200914262ElsevierBasic Parallel processesBisimulation equivalenceEquivalence checkingHereditary history preserving bisimilarityHistory preserving bisimilarityLabelled event structuresNon-interleaving equivalencesVerificationInformatikJournal Article10.1016/j.ic.2009.06.001Other