Bisimilarity is decidable in the union of normed BPA and normed BPP processes

Abstract

We compare the classes of behaviours (transition systems) which can be generated by normed BPA˙τ and normed BPP˙τ processes. We exactly classify the intersection of these two classes, i.e., the class of transition systems which can be equivalently (up to bisimilarity) described by the syntax of normed BPA˙τ and normed BPP˙τ processes. We provide such a characterization for classes of normed BPA and normed BPP processes as well.

Next we show that it is decidable in polynomial time whether for a given normed BPA˙τ (or BPP˙τ) process Δ there is some normed BPP˙τ (or BPA˙τ) process Δ such that Δ is bisimilar to Δ. Moreover, if the answer is positive then the process Δ can be effectively constructed. Simplified versions of the algorithms mentioned above for normed BPA and normed BPP are given too.

As an immediate (but important) consequence we also obtain decidability of bisimilarity in the union of normed BPA˙τ and normed BPP˙τ processes.