Homological properties of non-deterministic branchings and mergings in higher dimensional automata

Abstract

The branching (resp. merging) space functor of a flow is a left Quillen functor. The associated derived functor allows to define the branching (resp. merging) homology of a flow. It is then proved that this homology theory is a dihomotopy invariant and that higher dimensional branchings (resp. mergings) satisfy a long exact sequence.

24 pages and 6 figures ; cf http://www.emis.de/journals/HHA/

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• T-homotopy and refinement of observation (II) : Adding new T-homotopy equivalences
• Globular realization and cubical underlying homotopy type of time flow of process algebra
• The homology graph of a higher dimensional automaton
• T-homotopy and refinement of observation (V) : Strom model structure for branching and merging homologies
• Labeled homology of higher-dimensional automata
• Abstract homotopical methods for theoretical computer science