On the topology of concurrent systems

TL;DR

This paper demonstrates that any connected polyhedron can be represented as the homotopy type of a higher-dimensional automaton modeling a shared-variable concurrent system, linking topology with concurrency modeling.

Contribution

It establishes a correspondence between arbitrary connected polyhedra and the homotopy types of higher-dimensional automata for shared-variable systems, expanding the topological understanding of concurrency.

Findings

Any connected polyhedron can be realized as a higher-dimensional automaton's homotopy type.

The model captures the topological complexity of concurrent systems.

Provides a bridge between algebraic topology and concurrency theory.

Abstract

Higher-dimensional automata, i.e., pointed labeled precubical sets, are a powerful combinatorial-topological model for concurrent systems. In this paper, we show that for every (nonempty) connected polyhedron there exists a shared-variable system such that the higher-dimensional automaton modeling the state space of the system has the homotopy type of the polyhedron.