Subway Shuffle, 1 × 1 Rush Hour, and Cooperative Chess Puzzles: Computational Complexity of Puzzles
Name
Brunner-brunnerj-meng-eecs-2021-thesis.pdf
Description
Thesis PDF
Size
1.08 MB
Format
Adobe PDF
Checksum (MD5)
081674fd7844f74603209e50c7ebda47
Author(s)
Brunner, Josh
Advisor(s)
Demaine, Erik
Date Issued
June 2021
Publisher
Massachusetts Institute of Technology
Abstract
Oriented Subway Shuffle is a game played on a directed graph with colored edges and colored tokens present on some vertices. A move consists of moving a token across an edge of the matching color to an unoccupied vertex and reversing the orientation of that edge. The goal is to move a token across a target edge. We show that it is PSPACE-complete to determine whether a particular target edge can be moved across through a sequence of Oriented Subway Shuffle moves. We show how this can be interpreted in the context of the motion-planning-through-gadgets framework, thus showing PSPACE-completeness of certain motion planning problems. In contrast, we show that polynomial time suffices to determine whether a particular token can ever move.
This hardness result is motivated by three applications of proving other puzzles hard. A fairly straightforward reduction shows that the puzzle game Rush Hour is PSPACE-complete when all of the cars are 1 × 1 and there are fixed immovable cars. We show that two classes of cooperative Chess puzzles, helpmates and retrograde Chess, are also PSPACE-complete by reductions from Oriented Subway Shuffle.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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