Notes on Complexity of Bisimilarity between BPA and BPP

We consider the problem of deciding bisimilarity between a BPA process and a BPP process. This problem is known to be decidable, but no complexity bound has been provided so far. Our aim is to clarify the precise complexity and some related questions. In this short submission we present some preliminary results in this direction. In particular we present a necessary and sufficient condition for a BPP process to be bisimilar with some BPA process, which can be checked in polynomial space. In the positive case, (a modification of) the algorithm can transform the given BPP process into a special normal form (of exponential size) which can be easily converted into an equivalent BPA process. In this way, the problem of bisimilarity between BPA and BPP can be reduced to the problem of bisimilarity over BPA, which is known to be solvable in double exponential time.