منابع مشابه
The Three-Color and Two-Color TantrixTM Rotation Puzzle Problems Are NP-Complete Via Parsimonious Reductions
Holzer and Holzer [7] proved that the TantrixTM rotation puzzle problem with four colors is NP-complete, and they showed that the infinite variant of this problem is undecidable. In this paper, we study the three-color and two-color TantrixTM rotation puzzle problems (3-TRP and 2-TRP) and their variants. Restricting the number of allowed colors to three (respectively, to two) reduces the set of...
متن کاملSatisfiability Parsimoniously Reduces to the TantrixTM Rotation Puzzle Problem
Holzer and Holzer [HH04] proved that the Tantrix rotation puzzle problem is NP-complete. They also showed that for infinite rotation puzzles, this problem becomes undecidable. We study the counting version and the unique version of this problem. We prove that the satisfiability problem parsimoniously reduces to the Tantrix rotation puzzle problem. In particular, this reduction preserves the uni...
متن کاملMerkle Puzzles are Optimal
We prove that every key exchange protocol in the random oracle model in which the honest users make at most n queries to the oracle can be broken by an adversary making O(n) queries to the oracle. This improves on the previous Ω̃(n) query attack given by Impagliazzo and Rudich (STOC ’89). Our bound is optimal up to a constant factor since Merkle (CACM ’78) gave an n query key exchange protocol i...
متن کاملSpiral Galaxies Puzzles are NP-complete
We will show that the question of whether or not a given Spiral Galaxies puzzle has a solution is NP-complete. To do so, we construct Spiral Galaxies puzzles which correspond to arbitrary Boolean circuits. A circuit will be satisfied, (that is, have a set of inputs which give the desired outputs) if and only if the corresponding puzzle has a solution. Since Satisfiability is the canonical NP-co...
متن کاملPush-Pull Block Puzzles are Hard
This paper proves that push-pull block puzzles in 3D are PSPACE-complete to solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve, settling an open question [ZR11]. Pushpull block puzzles are a type of recreational motion planning problem, similar to Sokoban, that involve moving a ‘robot’ on a square grid with 1 × 1 obstacles. The obstacles cannot be traversed by the rob...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2004
ISSN: 0166-218X
DOI: 10.1016/j.dam.2003.11.011