Computational complexity of generalized push fight
Name
LIPIcs-FUN-2018-11.pdf
Description
Published version
Size
1.35 MB
Format
Adobe PDF
Checksum (MD5)
7a9e04783f1175c41ca289aa9df88924
Author(s)
Demaine, Erik
Date Issued
2018
Citation
Demaine, Erik. 2018. "Computational complexity of generalized push fight."
Version
Final published version
Abstract
© Jeffrey Bosboom, Erik D. Demaine, and Mikhail Rudoy; licensed under Creative Commons License CC-BY 9th International Conference on Fun with Algorithms (FUN 2018). 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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.FUN.2018.11
