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Time-reversal homotopical properties of concurrent systems
Homology, Homotopy and Applications ( IF 0.5 ) Pub Date : 2020-01-01 , DOI: 10.4310/hha.2020.v22.n2.a2
Cameron Calk 1 , Eric Goubault 1 , Philippe Malbos 2
Affiliation  

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.

中文翻译:

并发系统的时间反转同伦性质

有向拓扑被引入作为并发程序的模型,其中通过区分代表此类程序的拓扑空间中的某些路径来描述时间流。已经引入了尊重这种有向性的代数不变量来对有向空间进行分类。在这项工作中,我们研究了这种不变量在有向空间中时间流动逆转的性质。已知的不变量,自然同伦和同源性,已被证明在这种时间反转下保持不变。我们表明,这些可以配备额外的代数结构来见证这种逆转。具体来说,当应用于有向空间及其反转时,我们表明这些改进的不变量会产生对偶对象。
更新日期:2020-01-01
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