A DNA-based random walk method for solving k-SAT

  • Sergio Díaz
  • Juan Luis Esteban
  • Mitsunori Ogihara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2054)

Abstract

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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References

  1. [Adl94]
    L. Adleman. Molecular computation of solutions to combinatorial problems. Science, 266:1021–1024, 1994.CrossRefGoogle Scholar
  2. [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
  3. [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
  4. [Lip95]
    R. Lipton. DNA solutions of hard computational problems. Science, 268:542–545, 1995.CrossRefGoogle Scholar
  5. [LWF]
    Q. Liu, L. Wang, A. G. Frutos, R. M. Corn, and L. M. Smith. DNA computing on surfaces. Nature, 403:175–178, 2000. January, 13.CrossRefGoogle Scholar
  6. [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
  7. [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
  8. [OR99]
    M. Ogihara and A. Ray. Biomolecular computing— recent theoretical and experimental advances. SIGACT News, 30(2):22–30, 1999.CrossRefMathSciNetGoogle Scholar
  9. [ORS97]
    M. Ogihara, A. Ray, and K. Smith. Biomolecular computing— a shape of computation to come. SIGACT News, 28(3):2–11, 1997.CrossRefGoogle Scholar
  10. [Rob65]
    J. A. Robinson. A machine-oriented logic based on the resolution principle. Journal of the Association for Computing Machinery, 12(1):23–41, January 1965.MATHMathSciNetGoogle Scholar
  11. [ROMJ97]
    B. B. Rosenbaum, F. Oaks, S. Menchen, and B. Johnson. Improved single-stranded DNA sizing accuracy in capillary electrophoresis. Nucleic Acids Research, 25:3925–3929, 1997.CrossRefGoogle Scholar
  12. [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
  13. [SFM89]
    J. Sambrook, E. F. Fritsch, and T. Maniatis. Molecular Cloning: a Laboratory Manual. Cold Spring Harbor Press, NY, 2nd edition, 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Sergio Díaz
    • 1
  • Juan Luis Esteban
    • 1
  • Mitsunori Ogihara
    • 2
  1. 1.Dept. Llenguatges i sistemes informàticsUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Department of Computer ScienceUniversity of RochesterRochesterUSA

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