NP is as easy as detecting unique solutions
Theoretical Computer Science
SIAM Journal on Computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Tantrix TM rotation puzzles are intractable
Discrete Applied Mathematics - Fun with algorithms 2 (FUN 2001)
Tantrix: A Minute to Learn, 100 (Genetic Algorithm) Generations to Master
Genetic Programming and Evolvable Machines
IEEE Transactions on Computers
Satisfiability parsimoniously reduces to the Tantrix™ rotation puzzle problem
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
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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 available TantrixTM tiles from 56 to 14 (respectively, to 8). We prove that 3-TRP and 2-TRP are NP-complete, which answers a question raised by Holzer and Holzer [7] in the affirmative. Since our reductions are parsimonious, it follows that the problems Unique-3-TRP and Unique-2-TRP are DP-complete under randomized reductions. Finally, we prove that the infinite variants of 3-TRP and 2-TRP are undecidable.