Hugo Paquet - Bi-invariance for Uniform Strategies on Event Structures

entics:10498 - Electronic Notes in Theoretical Informatics and Computer Science, February 22, 2023, Volume 1 - Proceedings of MFPS XXXVIII -
Bi-invariance for Uniform Strategies on Event StructuresArticle

Authors: Hugo Paquet

    A recurring problem in game semantics is to enforce uniformity in strategies. Informally, a strategy is uniform when the Player's behaviour does not depend on the particular indexing of moves chosen by the Opponent. In game semantics, uniformity is used to define a resource modality !, that can be exploited for the semantics of programming languages. In this paper we give a new account of uniformity for strategies on event structures. This work is inspired by an older idea due to Melli├Ęs, that uniformity should be expressed as "bi-invariance" with respect to two interacting group actions. We explore the algebraic foundations of bi-invariance, adapt this idea to the language of event structures and define a general notion of uniform strategy in this context. Finally we revisit an existing approach to uniformity, and show how this arises as a special case of our constructions.

    Volume: Volume 1 - Proceedings of MFPS XXXVIII
    Published on: February 22, 2023
    Accepted on: December 16, 2022
    Submitted on: December 16, 2022
    Keywords: Computer Science - Logic in Computer Science,Mathematics - Category Theory


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