2014/09/20 by Uli Fahrenberg, Fahrenberg, Uli, Axel Legay +1
Computer Science · Mathematics · #Category Theory (math.CT) #FOS: Computer and information sciences #FOS: Mathematics #Geometric and Algebraic Topology #Logic in Computer Science (cs.LO) #Logic, programming, and type systems #cs.LO #math.CT #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1409.5865
Heavily revised version of arXiv:1209.4927
arxiv created 2014/09/20 · openalex publication_date 2014/09/20 · arxiv updated 2014/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new category of higher-dimensional automata in which the morphisms are functional homotopy simulations, i.e. functional simulations up to concurrency of independent events. For this, we use unfoldings of higher-dimensional automata into higher-dimensional trees. Using a notion of open maps in this category, we define homotopy bisimilarity. We show that homotopy bisimilarity is equivalent to a straight-forward generalization of standard bisimilarity to higher dimensions, and that it is finer than split bisimilarity and incomparable with history-preserving bisimilarity.