Comparing expressibility of normed BPA and normed BPP processes

Abstract

We present an exact characterization of those transition systems which can be equivalently (up to bisimilarity) defined by the syntax of normed BPA\(_\tau\) and normed BPP\(_\tau\) processes. We give such a characterization for the subclasses of normed BPA and normed BPP processes as well. Next we demonstrate the decidability of the problem whether for a given normed BPA\(_\tau\) process \(\Delta\) there is some unspecified normed BPP\(_\tau\) process \(\Delta'\) such that \(\Delta\) and \(\Delta'\) are bisimilar. The algorithm is polynomial. Furthermore, we show that if the answer to the previous question is positive, then (an example of) the process \(\Delta'\) is effectively constructible. Analogous algorithms are provided for normed BPP\(_\tau\) processes. Simplified versions of the mentioned algorithms which work for normed BPA and normed BPP are given too. As a simple consequence we obtain the decidability of bisimilarity in the union of normed BPA\(_\tau\) and normed BPP\(_\tau\) processes.