Complexity of Weak Bisimilarity and Regularity for BPA and BPP
| Authors | |
|---|---|
| Year of publication | 2003 |
| Type | Article in Periodical |
| Magazine / Source | Mathematical Structures in Computer Science |
| MU Faculty or unit | |
| 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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