{"title":"Symmetry in concurrent games","authors":"Simon Castellan, P. Clairambault, G. Winskel","doi":"10.1145/2603088.2603141","DOIUrl":null,"url":null,"abstract":"Behavioural symmetry is introduced into concurrent games. It expresses when plays are essentially the same. A characterization of strategies on games with symmetry is provided. This leads to a bi-category of strategies on games with symmetry. Symmetry helps allay the perhaps overly-concrete nature of games and strategies, and shares many mathematical features with homotopy. In the presence of symmetry we can consider monads for which the monad laws do not hold on the nose but do hold up to symmetry. This broadening of the concept of monad has a dramatic effect on the types concurrent games can support and allows us, for example, to recover the replication needed to express and extend traditional game semantics.","PeriodicalId":20649,"journal":{"name":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"50 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2014-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"34","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2603088.2603141","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 34

Abstract

Behavioural symmetry is introduced into concurrent games. It expresses when plays are essentially the same. A characterization of strategies on games with symmetry is provided. This leads to a bi-category of strategies on games with symmetry. Symmetry helps allay the perhaps overly-concrete nature of games and strategies, and shares many mathematical features with homotopy. In the presence of symmetry we can consider monads for which the monad laws do not hold on the nose but do hold up to symmetry. This broadening of the concept of monad has a dramatic effect on the types concurrent games can support and allows us, for example, to recover the replication needed to express and extend traditional game semantics.
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并发游戏中的对称性
行为对称被引入并发游戏中。它表达了戏剧在本质上是相同的。给出了对称博弈策略的表征。这就导致了对称游戏的双类策略。对称性有助于缓和游戏和策略过于具体的本质,并与同伦共享许多数学特征。在对称性存在的情况下,我们可以考虑单位体,单位体定律并不完全成立,但确实符合对称性。monad概念的扩展对并发游戏所支持的类型产生了巨大影响,例如,它允许我们恢复表达和扩展传统游戏语义所需的复制。
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