Solution of a 20-Variable 3-SAT Problem on a DNA Computer

Abstract

A 20-variable instance of the NP-complete three-satisfiability (3-SAT) problem was solved on a simple DNA computer. The unique answer was found after an exhaustive search of more than 1 million (2(20)) possibilities. This computational problem may be the largest yet solved by nonelectronic means. Problems of this size appear to be beyond the normal range of unaided human computation.

Writing Information into DNA

“…3 All of the strong constraints could be satisfied with only 3 bases [15]. Other groups that employed three-base words likewise used random word-generation for their word design [24,23].…”

Computing by polymerase chain reaction

“…He showed that an instance of a famous combinatorial problem can be translated in terms of DNA strands, put in a test tube in such a way that, by means of typical laboratory manipulations, a final DNA pool is obtained where the solution of the problem is encoded. Since then, a great deal of research has been carried on and many technical and theoretical achievements have been reached in DNA computing [12,[3][4][5]. Recently, new research perspectives have emerged that widen the possibilities of this field, among them: DNA self-assembly [21,22,15], DNA automata [2], and tools for DNA and RNA manipulation inspired by algorithmic analyses [17,11].…”

Problems on RNA Secondary Structure Prediction and Design

“…However, the authors state that "we lack a systematic a priori characterization of the class of configurations that this algorithm can solve". Another limitation of the algorithm is its high running time of Θ(n 6 ). An algorithm of Akutsu [1] runs in O(n 4 ) time and O(n 2 ) space, but there are natural pseudoknotted structures that cannot be handled by this algorithm.…”

“…The l i are not required to be equal. Complete combinatorial sets are also used to represent solution spaces in biocomputation that find a satisfying assignment to an instance of the Satisfiability problem [6,11]. Again, for this use, all strands in the complete combinatorial sets should form no secondary structure.…”