Laboratoire d'informatique de l'École polytechnique

Talk by Krzysztof Ziemiański: « Tracks in Higher Dimensional Automata »

Speaker: Krzysztof Ziemiański
Location: Online
Date: Wed, 23 Jun 2021, 11:00-12:00

For a new seminar of the proofs and algorithms pole of LIX, we are happy to welcome Krzysztof Ziemiański.

Abstract: The main goal of my talk is to present two models of executions of Higher Dimensional Automata. A track in a HDA is a sequence of cells such that every cell is either an upper face or an upper coface of the preceding one. To every track we can assign the (evi)pomset of its events; it is a labeled interval order equipped with an additional secondary ordering. Then we consider the set of tracks between fixed source and target cells, up to certain equivalence. This set is naturally a presheaf over the category of evipomsets, which is our first model of executions of HDA. This model can be simplified. When we restrict to step-sequence executions, ie, tracks in which the consecutive cells have only one common vertex, we obtain a presheaf over permutahedral category. This model is combinatorially simpler. At first glance it seems too restrictive but there is some evidence that this is not the case: the space of topological executions is homotopy equivalent to the geometric realization of the permutahedral model.

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