A random walk DNA algorithm for the 3-SAT problem

作者：Liu WB^*; Gao L; Zhang Q; Xu GD; Zhu XG; Liu XR; Jin X

来源：Current Nanoscience, 2005, 1(1): 85-90.

DOI：10.2174/1573413052953129

• DNA computing
• the satisfiability problem
• random walk strategy
• plasmids DNA

We present a randomized DNA algorithm for the 3-SAT problem based on the probabilistic algorithm proposed by Schoning. The basic idea of our algorithm is that the read of information is performed in linear DNA molecules, while the rewrite information is implemented in plasmid DNAs. Compared with previous works, our algorithm performs the flip of a variable';s value more easily and reliably, and the time complexity it, also reduced to O(mn), where m is the number of clauses and n is the number of variables. Moreover, Schoning';s algorithm has been further improved recently for the case of 3-SAT by Hofmeister. We also demonstrate how to adapt this improvement in our new algorithm and the space complexity of our algorithm is then reduced to O[(4/3)(n-3m) (7/3)(m)] where m is the number of the maximal independent clauses. Up to now, this is the most volume-efficient algorithm for the 3-SAT based on DNA computing.

• 出版日期2005-1
• 单位西安电子科技大学; 华中科技大学; 大连大学