A DNA-Based Algorithm for the Solution of Not-All-Equal 3-SAT Problem

• Published in: ICIE 2009 : 2009 WASE International Conference on Information Engineering :10-11 July 2009, Taiyuan, Shanxi, China Vol. 2; pp. 94 - 99
• Main Authors: Nung-Yue Shi, Chih-Ping Chu
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.07.2009
• Subjects: 3-SAT problem; Cities and towns; Computer science; Data mining; DNA; DNA-based Supercomputing; Key Words: Satisfiability problem; Molecular Solution; Not-All-Equal 3-SAT problem; NP-complete problem; Performance evaluation; Testing
• ISBN: 9780769536798; 0769536794
• DOI: 10.1109/ICIE.2009.57

Satisfiability problem is given a Boolean formula, and decide if a satisfying truth assignment exists. ((x 12 )macr or x 5 ) nland ((x 24 )macr or x 3 or (x 13 )macr or x 9 ) nland ... nland (x 12 ) nland (x 17 or x 8 or (x 18 )macr) is an example of Boolean formula. k-SAT means that each clause has exactly k literals. Not-all-equal (NAE) 3-SAT problem is defined by Garey and Johnson in 1979 as follows: There is a set V of variables and a collection C of clauses over V such that each clause has 3 literals. And the question is : Is there a truth assignment for V such that each clause has at least one true and at least one false literal? Note that the only difference with 3-SAT is that as well as one true literal, there must also be one false literal in each clause. In this paper, we will use molecular solution to find all true assignment (3 SAT problem) and furthermore find Not-All-Equal (NAE) solutions on DNA-based supercomputing. Finally, the simulated experiment is applied to verify correction of the proposed DNA-based algorithm for solving the not-all-equal 3-SAT problem.