Computational geometry: an introduction
Computational geometry: an introduction
The Othello game on an n × n board is PSPACE-complete
Theoretical Computer Science
SOKOBAN and other motion planning problems
Computational Geometry: Theory and Applications
Rush Hour is PSAPCE-complete, or "Why you should generously tip parking lot attendants"
Theoretical Computer Science
Complexity results for standard benchmark domains in planning
Artificial Intelligence
Tetris is hard, even to approximate
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
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A disentanglement puzzle consists of mechanically interlinked pieces, and the puzzle is solved by disentangling one piece from another set of pieces. A cast puzzle is a type of disentanglement puzzle, where each piece is a zinc die-casting alloy. In this paper, we consider the generalized cast puzzle problem whose input is the layout of a finite number of pieces (polyhedrons) in the 3-dimensional Euclidean space. For every integer k 驴 0, we present a polynomial-time transformation from an arbitrary k-exponential-space Turing machine M and its input x to a cast puzzle c 1 of size k-exponential in |x| such that M accepts x if and only if c 1 is solvable. Here, the layout of c 1 is encoded as a string of length polynomial (even if c 1 has size k-exponential). Therefore, the cast puzzle problem of size k-exponential is k-EXPSPACE-hard for every integer k 驴 0. We also present a polynomial-time transformation from an arbitrary instance f of the SAT problem to a cast puzzle c 2 such that f is satisfiable if and only if c 2 is solvable.