TY - JOUR

T1 - Time and space complexity for splicing systems

AU - Loos, Remco

AU - Ogihara, Mitsunori

N1 - Funding Information:
R. Loos work supported by Research Grants BES-2004-6316 and ES-2006-0146 of the Spanish Ministry of Education and Science.

PY - 2010/8

Y1 - 2010/8

N2 - 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.

AB - 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.

KW - Computational complexity

KW - DNA computing

KW - Splicing systems

UR - http://www.scopus.com/inward/record.url?scp=77952954895&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77952954895&partnerID=8YFLogxK

U2 - 10.1007/s00224-008-9161-7

DO - 10.1007/s00224-008-9161-7

M3 - Article

AN - SCOPUS:77952954895

VL - 47

SP - 301

EP - 316

JO - Theory of Computing Systems

JF - Theory of Computing Systems

SN - 1432-4350

IS - 2

ER -