Complexity of Weak Bisimilarity and Regularity for BPA and BPP

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Authors

SRBA Jiří

Year of publication 2003
Type Article in Periodical
Magazine / Source Mathematical Structures in Computer Science
MU Faculty or unit

Faculty of Informatics

Citation
Web http://www.brics.dk/~srba/publ.html
Field Informatics
Keywords weak bisimilarity; complexity; process algebra
Description It is an open problem whether weak bisimilarity is decidable for Basic Process Algebra (BPA) and Basic Parallel Processes (BPP). A PSPACE lower bound for BPA and NP lower bound for BPP were demonstrated by Stribrna. Mayr recently achieved a result, saying that weak bisimilarity for BPP is a hard problem for the second level of polynomial hierarchy. We improve this lower bound to PSPACE, moreover for the restricted class of normed BPP. Weak regularity (finiteness) of BPA and BPP is not known to be decidable either. In the case of BPP there is a hardness result for the second level of arithmetical hierarchy by Mayr, which we improve to PSPACE. No lower bound has previously been established for BPA. We demonstrate DP-hardness, which in particular implies both NP and coNP-hardness. In each of the bisimulation/regularity problems we consider also the classes of normed processes. Finally we show how the technique for proving co-NP lower bound for weak bisimilarity of BPA can be applied to strong bisimilarity of BPP.
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