On the topology of concurrent systems

2024/04/25 by Faustino, Catarina, Kahl, Thomas, Lopes, Rodrigo
#05E45 #55U10 #68Q85 #Algebraic Topology (math.AT) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Logic in Computer Science (cs.LO)

paper · doi:10.48550/arxiv.2404.16492

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.

Related

• The homology graph of a higher dimensional automaton
• Topological abstraction of higher-dimensional automata
• Labeled homology of higher-dimensional automata
• Trees in Partial Higher Dimensional Automata
• Mathematical Approach in Automata and Automata Association