Coalgebraic Multigames

Abstract : Coalgebraic games have been recently introduced as a generalization of Conway games and other notions of games arising in different contexts. Using coalgebraic methods, games can be viewed as elements of a final coalgebra for a suitable functor, and operations on games can be analyzed in terms of (generalized) coiteration schemata. Coalgebraic games are sequential in nature, i.e. at each step either the Left (L) or the Right (R) player moves (global polarization), moreover only a single move can be performed at each step. Recently, in the context of Game Semantics, concurrent games have been introduced, where global polarization is abandoned, and multiple moves are allowed. In this paper, we introduce coalgebraic multigames, which are situated half-way between traditional sequential games and concurrent games: global polarization is still present, however multiple moves are possible at each step, i.e. a team of L/R players moves in parallel. Coalgebraic operations, such as sum and negation, can be naturally defined on multigames. Interestingly, sum on coalgebraic multigames turns out to be related to Conway’s selective sum on games, rather than the usual (sequential) disjoint sum. Selective sum has a parallel nature, in that at each step the current player performs a move in at least one component of the sum game, while on disjoint sum the current player performs a move in exactly one component at each step. A monoidal closed category of coalgebraic multigames in the vein of a Joyal category of Conway games is then built. The relationship between coalgebraic multigames and games is then formalized via an equivalence of the multigame category and a monoidal closed category of coalgebraic games where tensor is selective sum.
Type de document :
Communication dans un congrès
Marcello M. Bonsangue. 12th International Workshop on Coalgebraic Methods in Computer Science (CMCS), Apr 2014, Grenoble, France. Lecture Notes in Computer Science, LNCS-8446, pp.33-49, 2014, Coalgebraic Methods in Computer Science. 〈10.1007/978-3-662-44124-4_3〉
Liste complète des métadonnées

Littérature citée [27 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01408751
Contributeur : Hal Ifip <>
Soumis le : lundi 5 décembre 2016 - 13:23:49
Dernière modification le : lundi 5 décembre 2016 - 15:34:56
Document(s) archivé(s) le : lundi 20 mars 2017 - 17:31:48

Fichier

328263_1_En_3_Chapter.pdf
Fichiers produits par l'(les) auteur(s)

Licence


Distributed under a Creative Commons Paternité 4.0 International License

Identifiants

Citation

Marina Lenisa. Coalgebraic Multigames. Marcello M. Bonsangue. 12th International Workshop on Coalgebraic Methods in Computer Science (CMCS), Apr 2014, Grenoble, France. Lecture Notes in Computer Science, LNCS-8446, pp.33-49, 2014, Coalgebraic Methods in Computer Science. 〈10.1007/978-3-662-44124-4_3〉. 〈hal-01408751〉

Partager

Métriques

Consultations de la notice

10

Téléchargements de fichiers

4