The switch operators and push-the-button games: a sequential compound over rulesets - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Theoretical Computer Science Année : 2018

The switch operators and push-the-button games: a sequential compound over rulesets

Résumé

We study operators that combine combinatorial games. This field was initiated by Sprague-Grundy (1930s), Milnor (1950s) and Berlekamp-Conway-Guy (1970-80s) via the now classical disjunctive sum operator on (abstract) games. The new class consists in operators for rulesets, dubbed the switch-operators. The ordered pair of rulesets (R 1 , R 2) is compatible if, given any position in R 1 , there is a description of how to move in R 2. Given compatible (R 1 , R 2), we build the push-the-button game R 1 R 2 , where players start by playing according to the rules R 1 , but at some point during play, one of the players must switch the rules to R 2 , by pushing the button ''. Thus, the game ends according to the terminal condition of ruleset R 2. We study the pairwise combinations of the classical rulesets Nim, Wythoff and Euclid. In addition, we prove that standard periodicity results for Subtraction games transfer to this setting, and we give partial results for a variation of Domineering, where R 1 is the game where the players put the domino tiles horizontally and R 2 the game where they play vertically (thus generalizing the octal game 0.07).
Fichier principal
Vignette du fichier
article_V9.pdf (865.96 Ko) Télécharger le fichier
rthlGrundy.jpg (170.39 Ko) Télécharger le fichier
rthlGrundyNB.jpg (120.54 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01566273 , version 1 (20-07-2017)
hal-01566273 , version 2 (20-12-2017)

Identifiants

Citer

Eric Duchene, Marc Heinrich, Urban Larsson, Aline Parreau. The switch operators and push-the-button games: a sequential compound over rulesets. Theoretical Computer Science, 2018, 715, pp.71-85. ⟨10.1016/j.tcs.2018.01.003⟩. ⟨hal-01566273v2⟩
277 Consultations
176 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More