Time and space complexity for splicing systems

Remco Loos, Mitsunori Ogihara

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)301-316
Number of pages16
JournalTheory of Computing Systems
Volume47
Issue number2
DOIs
StatePublished - Aug 1 2010

Keywords

  • Computational complexity
  • DNA computing
  • Splicing systems

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

Fingerprint Dive into the research topics of 'Time and space complexity for splicing systems'. Together they form a unique fingerprint.

  • Cite this