eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
17:1
17:14
10.4230/LIPIcs.ISAAC.2020.17
article
Complexity of Retrograde and Helpmate Chess Problems: Even Cooperative Chess Is Hard
Brunner, Josh
1
Demaine, Erik D.
1
https://orcid.org/0000-0003-3803-5703
Hendrickson, Dylan
1
https://orcid.org/0000-0002-9967-8799
Wellman, Julian
1
Computer Science and Artificial Intelligence Laboratory, MIT, Cambridge, MA, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol181-isaac2020/LIPIcs.ISAAC.2020.17/LIPIcs.ISAAC.2020.17.pdf
hardness
board games
PSPACE