History-Preserving Bisimilarity for Higher-Dimensional Automata via Open Maps

TL;DR

This paper characterizes history-preserving bisimilarity for higher-dimensional automata using open-maps, making it decidable for finite cases by leveraging the open-maps framework in the category of unfoldings of precubical sets.

Contribution

It provides a simple, transition-based characterization of history-preserving bisimilarity for higher-dimensional automata, enabling decidability results.

Findings

Decidability of history-preserving bisimilarity for finite higher-dimensional automata

A transition-based characterization using open-maps

Application of open-maps framework to unfoldings of precubical sets

Abstract

We show that history-preserving bisimilarity for higher-dimensional automata has a simple characterization directly in terms of higher-dimensional transitions. This implies that it is decidable for finite higher-dimensional automata. To arrive at our characterization, we apply the open-maps framework of Joyal, Nielsen and Winskel in the category of unfoldings of precubical sets.