并发策略作为Street纤维化
Concurrent Strategies as Street Fibrations
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中文总结 AI 辅助
本文刻画了并发博弈中两类具有恒等元的策略，证明弱等价类恰为诱导Street纤维化的策略，并建立了博弈与集合值预层范畴的联系。
中文摘要 AI 辅助
基于事件结构的并发博弈与策略是一种成熟且富有表现力的交互计算模型。在本文中，我们重新审视为该模型配备对称性的问题。对称性对于许多应用至关重要，但它也是数学复杂性的来源，尤其是因为带有对称性的策略可以在几种不同的等价概念下进行比较。我们的第一个贡献是完整刻画了两类策略，对于这两类策略，复合运算具有恒等元。对于这两类，恒等律分别相对于“弱”和“强”等价概念成立。主要结果是，弱类策略恰好对应于那些在博弈上诱导出Street纤维化的策略。我们还展示了既有的“薄”对称方法也适用于这一一般框架。第二个贡献是博弈与集合值预层范畴之间的形式联系。这延续了将博弈与关系模型联系起来的悠久传统，但此处还包含了一个非常一般的对称性模型。我们将策略刻画为Street纤维化，这使得与预层范畴的联系建立起来显著更加容易。
英文摘要
Concurrent games and strategies based on event structures are an established and expressive model of interactive computation. In this paper we revisit the problem of equipping this model with symmetry. Symmetry is essential for many applications, but it is also a source of mathematical complexity, not least because strategies with symmetry can be compared up to several distinct notions of equivalence. Our first contribution is a complete characterization of two classes of strategies for which composition admits an identity. For these two classes the identity laws hold, respectively, up to a "weak" and a "strong" notion of equivalence. The main result is that the weak class of strategies corresponds precisely to those inducing Street fibrations over the game. We also show how the established "thin" approach to symmetry also fits in this general framework. A second contribution is a formal connection between games and setoid-valued profunctors. This follows a long tradition of relating games and relational models, but here additionally includes a very general model of symmetries. Our characterization of strategies as Street fibrations makes the connection to profunctors significantly easier to establish.
发表机构
- Inria（法国国家数字技术研究所）
- École Normale Supérieure Paris（巴黎高等师范学院）
- Queen Mary University of London（伦敦大学玛丽女王学院）
机构由 AI 辅助整理，请以论文原文为准。
