Complexity of Weak Bisimilarity and Regularity for BPA and BPP

Abstract

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 have been
demonstrated by Stribrna. Mayr achieved recently a result, saying that
weak bisimilarity for BPP is Pi^P_2-hard. 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 Pi^P_2-hardness result 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 co-NP-hardness.
In each of the bisimulation/regularity problems we consider also the
classes of normed processes.