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.

翻译：博弈语义中的一个反复出现的问题是强化策略的均匀性。非正式地说，当参与者的行为不依赖于对手所选移动的特定索引时，该策略即为均匀的。在博弈语义中，均匀性用于定义资源模态算子 !，该算子可应用于编程语言的语义分析。本文针对事件结构上的策略均匀性提出了新的阐释。本研究受到Melliès提出的一个较早思想的启发，即均匀性应通过两个相互作用的群作用表达为"双不变性"。我们探究了双不变性的代数基础，将该思想适配到事件结构的语言框架中，并在此背景下定义了均匀策略的广义概念。最后，我们重新审视了现有的均匀性处理方法，并展示了其如何作为我们构造的特例而涌现。