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arXiv · 2212.07976

Bi-invariance for Uniform Strategies on Event Structures

Hugo Paquet
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Abstract

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\`es, 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.

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Hugo Paquet. 2022-12-15. Bi-invariance for Uniform Strategies on Event Structures. https://doi.org/10.46298/entics.10498

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