Technical Reports

The report FIMU-RS-2000-09

Some Remarks on Weak Bisimilarity of BPA-Processes

by Ivana Èerná, Jitka Støíbrná, December 2000, 26 pages.

FIMU-RS-2000-09. Available as Postscript, PDF.

Abstract:

The purpose of this work is to examine the decidability problem of weak bisimilarity for BPA-processes. It has been known that strong bisimilarity, which may be considered a special case of weak bisimilarity, where the internal (silent) action tau is treated equally to observable actions, is decidable for BPA-processes. For strong bisimilarity, these processes are finitely branching and so for two non-bisimilar processes there exists a level n that distinguishes the two processes. Additionally, from the decidability of whether two processes are equivalent at a given level n, semidecidability of strong non-bisimilarity directly follows. We examine the following two closely related approaches to semidecidability of strong equivalence:

1. construction of a (finite) bisimulation or expansion tree,
2. construction of a finite Caucal base.

We have attempted to find out if any of the above mentioned approaches could be generalized to (semi)decide weak bisimilarity. Our findings indicate that a direct generalization is not sufficient and an efficient (semi)decision procedure cannot be obtained in this way.