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Theory of Computing Systems

, Volume 47, Issue 2, pp 301–316 | Cite as

Time and Space Complexity for Splicing Systems

  • Remco Loos
  • Mitsunori Ogihara
Article
  • 66 Downloads

Abstract

In Loos and Ogihara (Theor. Comput. Sci., 386(1-2):132–150, 2007), time complexity for splicing systems has been introduced. This paper further explores the time complexity for splicing systems and in addition defines a notion of space complexity, which is based on the description size of the production tree of a word. It is then shown that all languages accepted by t(n) space-bounded nondeterministic Turing machines can be generated by extended splicing systems with a regular set of rules in time O(t(n)2). Combined with an earlier result, this shows that the class of languages generated by polynomially time bounded extended regular splicing systems is exactly PSPACE. As for space complexity, it is shown that there exists a finite k such that for every fully space-constructible function f(n) the languages produced by extended splicing systems with a regular set of rules having space complexity f(n) are accepted by O(f(n) k ) time bounded nondeterministic Turing machines. Also, it is shown that all languages accepted by f(n) time-bounded nondeterministic Turing machines can be generated by extended regular splicing systems in space O(f(n) k ). By combining these two results it is shown that the class of languages generated by extended splicing systems with a regular set of rules in polynomial space is exactly NP and that in exponential space is exactly NEXPTIME.

Keywords

DNA computing Splicing systems Computational complexity 

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References

  1. 1.
    Book, R.V.: Time-bounded grammars and their languages. J. Comput. Syst. Sci. 5(4), 397–429 (1971) MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Culik, K. II, Harju, T.: Splicing semigroups of dominoes and DNA. Discrete Appl. Math. 31, 261–277 (1991) MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Gladkiĭ, A.V.: On the complexity of derivations in phase-structure grammars. Algebra Logika Semin. 3(5-6), 29–44 (1964) (in Russian) Google Scholar
  4. 4.
    Head, T.: Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors. Bull. Math. Biol. 49, 737–759 (1987) MATHMathSciNetGoogle Scholar
  5. 5.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading (1979) MATHGoogle Scholar
  6. 6.
    Loos, R.: An alternative definition of splicing. Theor. Comput. Sci. 358, 75–87 (2006) MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Loos, R., Mitrana, V.: Non-preserving splicing with delay. Int. J. Comput. Math. 84(4), 427–436 (2007) MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Loos, R., Ogihara, M.: Complexity theory for splicing systems. Theor. Comput. Sci. 386(1-2), 132–150 (2007) MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Ogihara, M.: Relating the minimum model for DNA computation and Boolean circuits. In: Proceedings of the 1999 Genetic and Evolutionary Computation Conference, pp. 1817–1821. Morgan Kaufmann, San Francisco (1999) Google Scholar
  10. 10.
    Ogihara, M., Ray, A.: The minimum DNA computation model and its computational power. In: Unconventional Models of Computation, pp. 309–322. Springer, Singapore (1998) Google Scholar
  11. 11.
    Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994) MATHGoogle Scholar
  12. 12.
    Păun, Gh.: Regular extended H systems are computationally universal. J. Autom. Lang. Comb. 1(1), 27–36 (1996) MATHMathSciNetGoogle Scholar
  13. 13.
    Păun, Gh., Rozenberg, G., Salomaa, A.: Computing by splicing. Theor. Comput. Sci. 168(2), 321–336 (1996) MATHCrossRefGoogle Scholar
  14. 14.
    Păun, Gh., Rozenberg, G., Salomaa, A.: DNA Computing—New Computing Paradigms. Springer, Berlin (1998) MATHGoogle Scholar
  15. 15.
    Pixton, D.: Regularity of splicing languages. Discrete Appl. Math. 69, 101–124 (1996) MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Reif, J.H.: Parallel molecular computation. In: Proceedings of the 7th ACM Symposium on Parallel Algorithms and Architecture, pp. 213–223. ACM Press, New York (1995) Google Scholar
  17. 17.
    Savitch, W.J.: Relationships between nondeterministic and deterministic tape complexities. J. Comput. Syst. Sci. 4, 77–192 (1970) MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.European Bioinformatics InstituteEMBLCambridgeUK
  2. 2.Department of Computer ScienceUniversity of MiamiCoral GablesUSA

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