On Plain and Hereditary History-Preserving Bisimulation

Abstract

We investigate the difference between two well-known notions of<br />independence bisimilarity, history-preserving bisimulation and hereditary<br />history-preserving bisimulation. We characterise the difference between<br />the two bisimulations in trace-theoretical terms, advocating the<br />view that the first is (just) a bisimulation for causality, while the second<br />is a bisimulation for concurrency. We explore the frontier zone between<br />the two notions by defining a hierarchy of bounded backtracking bisimulations. <br />Our goal is to provide a stepping stone for the solution to<br />the intriguing open problem of whether hereditary history-preserving<br />bisimulation is decidable or not. We prove that each of the bounded<br />bisimulations is decidable. However, we also prove that the hierarchy<br />is strict. This rules out the possibility that decidability of the general<br />problem follows directly from the special case. Finally, we give a non-<br />trivial reduction solving the general problem for a restricted class of<br />systems and give pointers towards a full answer.