PSPACE-Completeness of Sliding-Block Puzzles and Other Problems through the Nondeterministic Constraint Logic Model of Computation
| dc.creator | Hearn, Robert A. | |
| dc.creator | Demaine, Erik D. | |
| dc.date | 2002-05-04 | |
| dc.date | 2004-11-11 | |
| dc.date.accessioned | 2026-07-26T00:01:18Z | |
| dc.description | We present a nondeterministic model of computation based on reversing edge directions in weighted directed graphs with minimum in-flow constraints on vertices. Deciding whether this simple graph model can be manipulated in order to reverse the direction of a particular edge is shown to be PSPACE-complete by a reduction from Quantified Boolean Formulas. We prove this result in a variety of special cases including planar graphs and highly restricted vertex configurations, some of which correspond to a kind of passive constraint logic. Our framework is inspired by (and indeed a generalization of) the ``Generalized Rush Hour Logic'' developed by Flake and Baum. We illustrate the importance of our model of computation by giving simple reductions to show that several motion-planning problems are PSPACE-hard. Our main result along these lines is that classic unrestricted sliding-block puzzles are PSPACE-hard, even if the pieces are restricted to be all dominoes (1x2 blocks) and the goal is simply to move a particular piece. No prior complexity results were known about these puzzles. This result can be seen as a strengthening of the existing result that the restricted Rush Hour puzzles are PSPACE-complete, of which we also give a simpler proof. Finally, we strengthen the existing result that the pushing-blocks puzzle Sokoban is PSPACE-complete, by showing that it is PSPACE-complete even if no barriers are allowed. | |
| dc.description | 19 pages, 16 figures. Version 4 adds token formulation and minor corrections. To appear in Theoretical Computer Science | |
| dc.identifier | https://arxiv.org/abs/cs/0205005 | |
| dc.identifier | http://arxiv.org/abs/cs/0205005 | |
| dc.identifier.uri | https://dspace.dare.co.zw/handle/123456789/103400 | |
| dc.subject | Computational Complexity | |
| dc.subject | Computer Science and Game Theory | |
| dc.subject | F.1; F.2.2 | |
| dc.title | PSPACE-Completeness of Sliding-Block Puzzles and Other Problems through the Nondeterministic Constraint Logic Model of Computation | |
| dc.type | text |