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Article Dans Une Revue Lecture Notes in Computer Science Année : 2020

A Dynamic Epistemic Logic Analysis of the Equality Negation Task

Marijana Lazić
  • Fonction : Auteur
Jérémy Ledent
Sergio Rajsbaum
  • Fonction : Auteur

Résumé

A semantics of concurrent programs can be given using precubical sets, in order to study (higher) commutations between the actions, thus encoding the "geometry" of the space of possible executions of the program. Here, we study the particular case of programs using only mutexes, which are the most widely used synchronization primitive. We show that in this case, the resulting programs have non-positive curvature, a notion that we introduce and study here for precubical sets, and can be thought of as an algebraic analogue of the well-known one for metric spaces. Using this it, as well as categorical rewriting techniques, we are then able to show that directed and non-directed homotopy coincide for directed paths in these precubical sets. Finally, we study the geometric realization of precubical sets in metric spaces, to show that our conditions on precubical sets actually coincide with those for metric spaces. Since the category of metric spaces is not cocomplete, we are lead to work with generalized metric spaces and study some of their properties.

Dates et versions

hal-04451597 , version 1 (11-02-2024)

Identifiants

Citer

Éric Goubault, Marijana Lazić, Jérémy Ledent, Sergio Rajsbaum. A Dynamic Epistemic Logic Analysis of the Equality Negation Task. Lecture Notes in Computer Science, 2020, Lecture Notes in Computer Science, 12005, pp.53-70. ⟨10.1007/978-3-030-38808-9_4⟩. ⟨hal-04451597⟩
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