Computational Complexity of Generalized Push Fight

Jeffrey Bosboom; Erik D. Demaine; Mikhail Rudoy

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arXiv · 1803.03708

Computational Complexity of Generalized Push Fight

Jeffrey Bosboom·Erik D. Demaine·Mikhail Rudoy

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Abstract

We analyze the computational complexity of optimally playing the two-player board game Push Fight, generalized to an arbitrary board and number of pieces. We prove that the game is PSPACE-hard to decide who will win from a given position, even for simple (almost rectangular) hole-free boards. We also analyze the mate-in-1 problem: can the player win in a single turn? One turn in Push Fight consists of up to two "moves" followed by a mandatory "push". With these rules, or generalizing the number of allowed moves to any constant, we show mate-in-1 can be solved in polynomial time. If, however, the number of moves per turn is part of the input, the problem becomes NP-complete. On the other hand, without any limit on the number of moves per turn, the problem becomes polynomially solvable again.

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Jeffrey Bosboom, Erik D. Demaine, Mikhail Rudoy. 2018-03-09. Computational Complexity of Generalized Push Fight. https://arxiv.org/abs/1803.03708

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