Abstract
It is an open problem whether weak bisimilarity is decidable<br />for Basic Process Algebra (BPA) and Basic Parallel Processes (BPP). A<br />PSPACE lower bound for BPA and NP lower bound for BPP have been<br />demonstrated by Stribrna. Mayr achieved recently a result, saying that<br />weak bisimilarity for BPP is Pi^P_2-hard. We improve this lower bound to<br />PSPACE, moreover for the restricted class of normed BPP.<br />Weak regularity (finiteness) of BPA and BPP is not known to be decidable<br />either. In the case of BPP there is a Pi^P_2-hardness result by Mayr,<br />which we improve to PSPACE. No lower bound has previously been established<br />for BPA. We demonstrate DP-hardness, which in particular<br />implies both NP and co-NP-hardness.<br />In each of the bisimulation/regularity problems we consider also the<br />classes of normed processes.
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