Homotopy Bisimilarity for Higher-Dimensional Automata

Uli Fahrenberg; Axel Legay

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arXiv · 1409.5865

Homotopy Bisimilarity for Higher-Dimensional Automata

Uli Fahrenberg·Axel Legay

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Abstract

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.

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Uli Fahrenberg, Axel Legay. 2014-09-20. Homotopy Bisimilarity for Higher-Dimensional Automata. https://arxiv.org/abs/1409.5865

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