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)


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.


Turing Machine Transition Rule Rectangular Hole Simple Polyhedron Tape Cell 
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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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