A DNA-based random walk method for solving k-SAT
This paper presents an implementation of a concurrent version of Schöning’s algorithm for k-SAT in [Sch99]. It is shown that the algorithm can be implemented with space complexity O((2 − 2/k )n) and time complexity O(kmn + n3), where n is the number of variables and m the number of clauses. Besides, borrowing ideas from the above mentioned implementation, it is presented an implementation of resolution, a widely studied and used proof system, mainly in the fields of Proof Complexity and Automated Theorem Proving.
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- [BCGT96]E. Bach, A. Condon, E. Glaser, and C. Tanguay. DNA models and algorithms for NP-complete problems. In Proceedings of 11th Conference on Computational Complexity, pages 290–299. IEEE Computer Society Press, Los Alamitos, CA, 1996.Google Scholar
- [CCC97]W. Cai, A. Condon, R. Corn, E. Glaser, Z. Fei, T. Frutos, Z. Guo, M. Lagally, Q. Liu, L. Smith, and A. Thiel. The power of surface-based DNA computation. In Proceedings of 1st International Conference on Computational Molecular Biology, pages 67–74. ACM Press, 1997.Google Scholar
- [Ogi96]M. Ogihara. Breadth first search 3SAT algorithms for DNA computers. Technical Report TR 629, Department of Computer Science, University of Rochester, Rochester, NY, July 1996.Google Scholar
- [OR97]M. Ogihara and A. Ray. DNA-based parallel computation by counting. In H. Rubin and D. H. Wood, editors, DNA Based Computers III, pages 255–264, 1997.Google Scholar
- [Sch99]U. Schöning. A probabilistic algorithm for k-SAT and constraint satisfaction problems. In Proceedings of 40th Symposium on Foundations of Computer Science, pages 410–414. IEEE Computer Society Press, Los Alamitos, CA, 1999.Google Scholar
- [SFM89]J. Sambrook, E. F. Fritsch, and T. Maniatis. Molecular Cloning: a Laboratory Manual. Cold Spring Harbor Press, NY, 2nd edition, 1989.Google Scholar