Tantrix TM rotation puzzles are intractable

Authors:
Markus Holzer;Waltraud Holzer
Affiliations:
Institut für Informatik, Technische Universität München, Arcisstraße 21, D-80290 München, Germany and Département d'I.R.O., Université de Montréal, Canada;Birkenstraße 27, D-82024 Taufkirchen, Germany
Venue:
Discrete Applied Mathematics - Fun with algorithms 2 (FUN 2001)
Year:
2004

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Abstract

It is shown that the TANTRIXTM rotation puzzle can be used to emulate a circuit with AND- and NOT-gates. In particular, a rotation puzzle is constructed, that has a solution if and only if there exists an assignment to the input variables such that the corresponding circuit evaluates to true. This shows that the rotation puzzle is intractable, i.e., NP-complete. Moreover, we also consider infinite TANTRIXTM rotation puzzles. Based on a circuit construction, too, we show that in this case the problem becomes even worse, namely undecidable.