منابع مشابه
Invariant games
In the context of 2-player removal games, we define the notion of invariant game for which each allowed move is independent of the position it is played from. We present a family of invariant games which are variations of Wythoff’s game. The set of P -positions of these games are given by a pair of complementary Beatty sequences related to the irrational quadratic number αk = (1; 1, k). We also...
متن کاملOn Invariant Games
A 2-pile take-away game is played by two players who alternate in removing tokens from two piles according to given rules. The game is invariant if if the same moves can be played from any game position, provided only that there are enough tokens in the piles. Duchêne and Rigo in a paper in this issue conjectured that if the second player winning positions are given by a pair of complementary h...
متن کاملInvariant Projections in Games
Identification of implicit structures in dynamic systems is a fundamental problem in Artificial Intelligence. In this paper, we focus on General Game Playing where games are modeled as finite state machines. We define a new property of game states called invariant projections which strongly corresponds to humans’ intuition of game boards and may be applied in General Game Playing to support pow...
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 کاملInvariant games and non-homogeneous Beatty sequences
We characterize all the pairs of complementary non-homogenous Beatty sequences (An) n≥0 and (Bn) n≥0 for which there exists an invariant game having exactly {(An, Bn) | n ≥ 0} ∪ {(Bn, An) | n ≥ 0} as set of P-positions. Using the notion of Sturmian word and tools arising in symbolic dynamics and combinatorics on words, this characterization can be translated to a decision procedure relying only...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2010
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2010.05.007