Hereditary History Preserving Simulation is Undecidable

Abstract

We show undecidability of hereditary history preserving simulation<br />for finite asynchronous transition systems by a reduction from the halting<br />problem of deterministic Turing machines. To make the proof more<br />transparent we introduce an intermediate problem of deciding the winner<br />in domino snake games. First we reduce the halting problem of deterministic<br />Turing machines to domino snake games. Then we show how to<br />model a domino snake game by a hereditary history simulation game on<br />a pair of finite asynchronous transition systems.