Complexity of retrograde and helpmate chess problems: Even cooperative chess is hard
Name
LIPIcs-ISAAC-2020-17.pdf
Description
Published version
Size
743.91 KB
Format
Adobe PDF
Checksum (MD5)
897df08864be6d0154e8158221a0d33c
Author(s)
Brunner, J
Demaine, ED
Hendrickson, D
Wellman, J
Date Issued
December 1, 2020
Journal
Leibniz International Proceedings in Informatics, LIPIcs
Citation
Brunner, J, Demaine, ED, Hendrickson, D and Wellman, J. 2020. "Complexity of retrograde and helpmate chess problems: Even cooperative chess is hard." Leibniz International Proceedings in Informatics, LIPIcs, 181.
Version
Final published version
Abstract
We prove PSPACE-completeness of two classic types of Chess problems when generalized to n × n boards. A “retrograde” problem asks whether it is possible for a position to be reached from a natural starting position, i.e., whether the position is “valid” or “legal” or “reachable”. Most real-world retrograde Chess problems ask for the last few moves of such a sequence; we analyze the decision question which gets at the existence of an exponentially long move sequence. A “helpmate” problem asks whether it is possible for a player to become checkmated by any sequence of moves from a given position. A helpmate problem is essentially a cooperative form of Chess, where both players work together to cause a particular player to win; it also arises in regular Chess games, where a player who runs out of time (flags) loses only if they could ever possibly be checkmated from the current position (i.e., the helpmate problem has a solution). Our PSPACE-hardness reductions are from a variant of a puzzle game called Subway Shuffle.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution 3.0 unported license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.ISAAC.2020.17
