منابع مشابه
Ultimately bipartite subtraction games
We introduce the notion of ultimately bipartite impartial games. These are games that are ultimately periodic in the simplest possible manner. We examine ultimately bipartite subtraction games and demonstrate a curious feature: for ‘large’ games it is clear who has the winning position and how the game should be strategically played, but during play, as the game eventually becomes small, it is ...
متن کاملAperiodic Subtraction Games
Periodicity is a fundamental property of many combinatorial games. It is sought vigorously, yet remains elusive in important cases, such as for some octal games, notably Grundy’s game. Periodicity is important, because it provides poly-time winning strategies for many games. In particular, subtraction games, impartial and partizan, have been proved to be periodic. Our main purpose here is to ex...
متن کاملThe *-operator and invariant subtraction games
An invariant subtraction game is a 2-player impartial game defined by a set of invariant moves (k-tuples of non-negative integers) M. Given a position (another k-tuple) x = (x1, . . . , xk), each option is of the form (x1 − m1, . . . , xk − mk), where m = (m1, . . . ,mk) ∈ M (and where xi − mi ≥ 0, for all i). Two players alternate in moving and the player who moves last wins. The set of non-ze...
متن کاملA New Algorithm for the Subtraction Games
Subtraction games is a class of combinatorial games. It was solved since the Sprague-Grundy Theory was put forward. This paper described a new algorithm for subtraction games. The new algorithm can find win or lost positions in subtraction games. In addition, it is much simpler than Sprague-Grundy Theory in one pile of the games.
متن کاملThe Period of the subtraction games
Subtraction games is a class of impartial combinatorial games, They with finite subtraction sets are known to have periodic nim-sequences. So people try to find the regular of the games. But for specific of Sprague-Grundy Theory, it is too difficult to find, they obtained some conclusions just by simple observing. This paper used PTFN algorithm to analyze the period of the Subtraction games. It...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/7904