Time and Space Complexity for Splicing Systems
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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.
KeywordsDNA computing Splicing systems Computational complexity
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- 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
- 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.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
- 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