On the computational complexity of portal and push-pull block puzzles

We classify the computational complexity of two types of motion planning problems represented in games. Portal, a popular video game, is shown to be NP-hard or PSPACE-complete depending on the game mechanics allowed. Push-pull block puzzles are games, similar to Sokoban, which involve moving a 'robot' on a square grid with obstacles and blocks that can be pushed or pulled by the robot into adjacent squares. We prove that push-pull block puzzles in 3D and push-pull block puzzles in 2D with thin walls are NP-hard to solve. We also show certain 3D push-pull block puzzles are PSPACE-complete. This work follows in a long line of algorithms and complexity work on similar problems Wil91, DDO00, Hof00, DHH04, DH01, DO92, DHH02, Cul98, DZ96, Rit10]. The 2D push-pull block puzzle also shows up in a number of video games, thus implying other results, further continuing the work on understanding video games as in Vig12, ADGV14, For10, Cor04.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2015

Author dc:creator

• Lynch, Jayson (Jayson R.)

Advisor dc:contributor.advisor

• Erik Demaine.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/105999

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/105999