Hereditary History Preserving Bisimilarity is Undecidable

Abstract

We show undecidability of hereditary history preserving bisimilarity<br />for finite asynchronous transition systems by a reduction from the halting<br />problem of deterministic 2-counter machines. To make the proof more<br />transparent we introduce an intermediate problem of checking domino<br />bisimilarity for origin constrained tiling systems. First we reduce the<br />halting problem of deterministic 2-counter machines to origin constrained<br />domino bisimilarity. Then we show how to model domino bisimulations as<br />hereditary history preserving bisimulations for finite asynchronous transitions<br />systems. We also argue that the undecidability result holds for<br />finite 1-safe Petri nets, which can be seen as a proper subclass of finite<br />asynchronous transition systems.