Computational complexity of string puzzles

Authors:
Chuzo Iwamoto;Kento Sasaki;Kenichi Morita
Affiliations:
Hiroshima University, Higashi-Hiroshima, Japan;Hiroshima University, Higashi-Hiroshima, Japan;Hiroshima University, Higashi-Hiroshima, Japan
Venue:
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
Year:
2012

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Abstract

A disentanglement puzzle consists of mechanically interlinked pieces, and the puzzle is solved by disentangling one piece from another set of pieces. A string puzzle is a type of disentanglement puzzle, which consists of strings entangled with one or more wooden pieces. In this paper, we consider the generalized string puzzle problem whose input is the layout of strings and a wooden board with holes embedded in the 3-dimensional Euclidean space. We present a polynomial-time transformation from an arbitrary instance f of the 3SAT problem to a string puzzle s such that f is satisfiable if and only if s is solvable. Therefore, the generalized string puzzle problem is NP-hard.