Skip to main content
SpringerLink
Log in

Molecular computing, bounded nondeterminism, and efficient recursion

  • Session 21: Biocomputing
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1256))

Included in the following conference series:

Abstract

The maximum number of strands used is an important measure of a molecular algorithm's complexity. This measure is also called the space used by the algorithm. We show that every NP problem that can be solved with b(n) bits of nondeterminism can be solved by molecular computation in a polynomial number of steps, with four test tubes, in space 2b(n. In addition, we identify a large class of recursive algorithms that can be implemented using bounded nondeterminism. This yields improved molecular algorithms for important problems like 3-SAT, independent set, and 3-colorability.

Research supported in part by the National Science Foundation under grants CCR-8958528 and CCR-9415410 and by NASA under grant NAG 52895. On sabbatical from Yale University.

Research supported in part by the National Science Foundation under grants CCR-8958528 and CCR-9415410.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Adleman. Molecular computation of solutions to combinatorial problems. Science, 266:1021–1024, Nov. 1994.

    PubMed  Google Scholar 

  2. L. Adleman. On constructing a molecular computer. In 1st DIMACS workshop on DNA Computing, 1995.

    Google Scholar 

  3. E. Bach, A. Condon, E. Glaser, and C. Tanguay. DNA models and algorithms for NP-complete problems. In Proc. 11th Ann. Conf. Structure in Complexity Theory, pp. 290–299, 1996.

    Google Scholar 

  4. D. Beaver. A universal molecular computer. CSE 95-001, Penn. State Univ., 1995.

    Google Scholar 

  5. R. Beigel. Maximum independent set algorithms. Manuscript, 1996.

    Google Scholar 

  6. R. Beigel and D. Eppstein. 3-coloring in time O(1.3446n): a no-MIS algorithm. In Proc. 36th IEEE FOCS, pp. 444–452, 1995.

    Google Scholar 

  7. R. Beigel and J. Goldsmith. Downward separation fails catastrophically for limited nondeterminism classes. In Proc. 9th Ann. Conf. Structure in Complexity Theory, pp. 134–138, 1994.

    Google Scholar 

  8. D. Boneh, C. Dunworth, R. J. Lipton, and J. Sgall. On the computational power of DNA. Manuscript, 1996.

    Google Scholar 

  9. J. F. Buss and J. Goldsmith. Nondeterminism within P. SICOMP, 22:560–572, 1993.

    Google Scholar 

  10. J. D. C. Àlvarez and J. Torán. Complexity classes with complete problems between P and NP-complete. In Foundations of Computation Theory, pp. 13–24. Springer-Verlag, 1989. LNCS 380.

    Google Scholar 

  11. J. Díaz and J. Torán. Classes of bounded nondeterminism. MST, 23:21–32, 1990.

    Google Scholar 

  12. J. Goldsmith, M. Levy, and M. Mundhenk. Limited nondeterminism. SIGACT News, pp. 20–29, June 1996.

    Google Scholar 

  13. L. Hemachandra and S. Jha. Defying upward and downward separation. In Proc. 10th STACS, pp. 185–195. Springer-Verlag, 1993. LNCS 665.

    Google Scholar 

  14. C. M. R. Kintala. Computations with a restricted number of nondeterministic steps. PhD thesis, Penn. State Univ., University Park, PA, 1977.

    Google Scholar 

  15. C. M. R. Kintala and P. C. Fischer. Computations with a restricted number of nondeterministic steps. In Proc. 9th A CM STOC, pp. 178–185, 1977.

    Google Scholar 

  16. C. M. R. Kintala and P. C. Fischer. Refining nondeterminism in relativized polynomial-time bounded computations. SICOMP, 9(1):46–53, Feb. 1980.

    Google Scholar 

  17. R. Lipton. Using DNA to solve NP-complete problems. Science, 268:542–545, Apr. 1995.

    PubMed  Google Scholar 

  18. B. Monien and E. Speckenmeyer. Solving satisfiability in less than 2n steps. Discrete Appl. Math., 10:287–295, 1985.

    Article  Google Scholar 

  19. M. Ogihara. Breadth first search 3SAT algorithms for DNA computers. TR 629, U. Rochester, July 1996.

    Google Scholar 

  20. C. H. Papadimitriou and M. Yannakakis. On limited nondeterminism and the complexity of the V-C dimension. In Proc. 8th Ann. Conf. Structure in Complexity Theory, pp. 12–18, 1993.

    Google Scholar 

  21. N. Pippenger and M. Fischer. Relations among complexity measures. J. ACM, 26, 1979.

    Google Scholar 

  22. J. Robson. Algorithms for maximum independent sets. J. Algorithms, 7:425–440, 1986.

    Article  Google Scholar 

  23. D. Roos and K. Wagner. On the power of bio-computers. TR, U. of Wurzburg, Feb. 1995. ftp://haegar.informatik.uni-wuerzburg.de/pub/TRs/ro-wa95.ps.gz.

    Google Scholar 

  24. P. Rothemund. A DNA and restriction enzyme implementation of Turing machines. http://www.ugcs.caltech.edu/tt∼pwkr/oett.html.

    Google Scholar 

  25. L. Sanchis. Constructing language instances based on partial information. International Jour. Found. Comp. Sci., 5(2):209–229, 1994.

    Article  Google Scholar 

  26. I. Schiermeyer. Pure literal lookahead: An O(l,497n) 3-satisfiability algorithm. Manuscript, August 14, 1996.

    Google Scholar 

  27. C. P. Schnorr. Optimal algorithms for self-reducible problems. In Proc. 3rd ICALP, pp. 322–337, 1976.

    Google Scholar 

  28. A. L. Selman. Natural self-reducible sets. TR, Northeastern Univ., 1986.

    Google Scholar 

  29. W. Smith and A. Schweitzer. DNA computers in vitro and vivo. TR, NEC, 1995.

    Google Scholar 

  30. R. Tarjan. Finding a maximum clique. TR 72-123, Cornell Univ., 1972.

    Google Scholar 

Download references

Author information

Author notes

  1. Richard Beigel

    Present address: Dept. of Computer Science, University of Maryland at College Park, 20742-3251, College Park, MD, USA

  2. Bin Fu

    Present address: Dept. of Computer Science, P.O. Box 208285, 06520-8285, New Haven, CT, USA

Authors and Affiliations

  1. Yale University, University of Maryland, and Lehigh University, USA

    Richard Beigel

  2. Yale University and University of Maryland, USA

    Bin Fu

Authors
  1. Richard Beigel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bin Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Richard Beigel or Bin Fu .

Editor information

Pierpaolo Degano Roberto Gorrieri Alberto Marchetti-Spaccamela

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Beigel, R., Fu, B. (1997). Molecular computing, bounded nondeterminism, and efficient recursion. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_234

Download citation

  • DOI: https://doi.org/10.1007/3-540-63165-8_234

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63165-1

  • Online ISBN: 978-3-540-69194-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation