Exhaustive search and hardness proofs for games
Name
1227516732-MIT.pdf
Size
11.54 MB
Format
Adobe PDF
Checksum (MD5)
8d2bdde9aaced3d58a54925f3428281f
Author(s)
Bosboom, Jeffrey(Jeffrey William)
Advisor(s)
Erik D. Demaine.
Date Issued
2020
Publisher
Massachusetts Institute of Technology
Abstract
This thesis explores several games from two perspectives: exhaustive search and hardness proofs. First, we present an exhaustive search for hardness proofs: a system for finding motion planning simulations. Second, we prove that the pencil-and-paper puzzle Tatamibari is NP-complete, a proof developed using a Tatamibari solver we wrote based on the Z3 SMT solver. Third, we find by computer search that the board game Push Fight played on a board with one column (four squares) removed is a draw. Then we prove that mate-in-1 in generalized Push Fight is NP-complete and that determining the winner of a game in progress is PSPACE-hard. Fourth, we prove that path puzzles are NP-complete, ASP-complete, and #P-complete. We describe a solver for path puzzles based on depth-first search that solves 14 of 15 puzzles from the last chapter of the path puzzles book. Fifth, we present a nonogram solver based on automaton intersection. Relatedly, we prove that finding an optimal automaton intersection ordering is PSPACE-hard. Sixth, we analyze puzzles from the video game The Witness and obtain NP-completeness for most clue types and [sigma]₂-completeness for puzzles containing antibody clues. Finally, we propose a generic framework for parsing screenshots of grid-based video games.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, September, 2020
Cataloged from student-submitted PDF of thesis.
Includes bibliographical references (pages 275-289).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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