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Computational Complexity of Cast Puzzles

  • Chuzo Iwamoto
  • Kento Sasaki
  • Kenji Nishio
  • Kenichi Morita
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)

Abstract

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 ≥ 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 ≥ 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.

Keywords

Turing Machine Transition Rule Rectangular Hole Simple Polyhedron Tape Cell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Chuzo Iwamoto
    • 1
  • Kento Sasaki
    • 1
  • Kenji Nishio
    • 2
  • Kenichi Morita
    • 1
  1. 1.Graduate School of EngineeringHiroshima UniversityHigashi-HiroshimaJapan
  2. 2.Sharp CorporationOsakaJapan

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