Decidability of Plain and Hereditary History-Preserving Bisimilarity for BPP

Abstract

In this paper we investigate the decidability of history-preserving bisimilarity (HPB) and hereditary history-preserving bisimilarity (HHPB) for basic parallel processes (BPP). We find that both notions are decidable for this class of infinite systems, and present tableau-based decision procedures. The first result is not new but has already been established via the decidability of causal bisimilarity, a notion that is equivalent to HPB. We shall see that our decision procedure is similar to Christensen's proof of the decidability of distributed bisimilarity, which leads us to the coincidence between HPB and distributed bisimilarity for BPP. The decidability of HHPB is a new result. This result is especially interesting, since the decidability of HHPB for finite-state systems has been a long-standing open problem which has recently been shown to be undecidable.