Discovering a new universal partizan ruleset

Abstract

In Combinatorial Game Theory, we study the set of games G, whose elements are mapped from positions of rulesets. In many case, given a ruleset, not all elements of G can be given as a position in the ruleset. It is an intriguing question what kind of ruleset would allow all of them to appear. In this paper, we introduce a ruleset named turning tiles and prove the ruleset is a universal partizan ruleset, that is, every element in G can occur as a position in the ruleset. This is the second universal partizan ruleset after generalized konane.

New universal partizan rulesets

“…Early results showed that generalized konane and turning tiles are universal partizan ruleset ( [2,4]). In this study, we will use the latter ruleset.…”

Winner Determination Algorithms for Graph Games with Matching Structures

“…The notion of a universal ruleset is defined in [1], and the same paper proves that Generalized Konane is a universal ruleset. The ruleset that was secondarily shown to be universal is Turning Tiles and since then, two other rulesets were also shown to be universal by (polynomial-time) reductions from Turning Tiles [4,5]. The universality of a game implies that it is sufficiently complex.…”