The nondeterministic constraint logic model of computation: Reductions and applications

Abstract

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 andhighly restrictedv ertex configurations, some of which correspondto a kindof passive constraint logic. Our framework is inspired by (andind eeda generalization of) the "GeneralizedRush Hour Logic" developedb y Flake andBaum [2]. We illustrate the importance of our model of computation by giving simple reductions to show that multiple 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 restrictedto be all dominoes (1×2 blocks) andthe 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 restrictedRush HourTM puzzles are PSPACE-complete [2], of which we also give a simpler proof. Finally, we strengthen the existing result that the pushing-blocks puzzle Sokoban is PSPACE-complete [1], by showing that it is PSPACE-complete even if no barriers are allowed. © 2002 Springer-Verlag Berlin Heidelberg.