Rush Hour is PSAPCE-complete, or "Why you should generously tip parking lot attendants"
Theoretical Computer Science
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Relationships between nondeterministic and deterministic tape complexities
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ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
The kissing problem: how to end a gathering when everyone kisses everyone else goodbye
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
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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 restrictedv ertex 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 [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脳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 restricted Rush Hour驴 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.