Time-reversal homotopical properties of concurrent systems - Archive ouverte HAL Access content directly
Journal Articles Homology, Homotopy and Applications(HHA) Year : 2020

Time-reversal homotopical properties of concurrent systems

Abstract

Directed topology was introduced as a model of concurrent programs, where the flow of time is described by distinguishing certain paths in the topological space representing such a program. Algebraic invariants which respect this directedness have been introduced to classify directed spaces. In this work we study the properties of such invariants with respect to the reversal of the flow of time in directed spaces. Known invariants, natural homotopy and homology, have been shown to be unchanged under this time-reversal. We show that these can be equipped with additional algebraic structure witnessing this reversal. Specifically, when applied to a directed space and to its reversal, we show that these refined invariants yield dual objects. We further refine natural homotopy by introducing a notion of relative directed homotopy and showing the existence of a long exact sequence of natural homotopy systems.
Fichier principal
Vignette du fichier
timeReversal.pdf (361.97 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02015088 , version 1 (12-02-2019)

Identifiers

Cite

Cameron Calk, Éric Goubault, Philippe Malbos. Time-reversal homotopical properties of concurrent systems. Homology, Homotopy and Applications(HHA), 2020, 22 (2), pp.31-57. ⟨10.4310/HHA.2020.v22.n2.a2⟩. ⟨hal-02015088⟩
134 View
97 Download

Altmetric

Share

Gmail Facebook X LinkedIn More