Abstract
This paper proposes a notion of time complexity in splicing systems and presents fundamental properties of SPLTIME, the class of languages with splicing system time complexity t(n). Its relations to classes based on standard computational models are explored. It is shown that for any function t(n), SPLTIME[t(n)] is included in 1NSPACE[t(n)]. Expanding on this result, 1NSPACE[t(n)] is characterized in terms of splicing systems: it is the class of languages accepted by a t(n)-space uniform family of extended splicing systems having production time O(t(n)) with regular rules described by finite automata with at most a constant number of states. As to lower bounds, it is shown that for all functions t(n) ≥ logn, all languages accepted by a pushdown automaton with maximal stack height t(|x|) for a word x are in SPLTIME[t(n)]. From this result, it follows that the regular languages are in SPLTIME[O(log(n))] and that the context-free languages are in SPLTIME[O(n)].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Book, R.V.: Time-bounded grammars and their languages. Journal of Computer and System Sciences 5(4), 397–429 (1971)
Culik II, K., Harju, T.: Splicing semigroups of dominoes and DNA. Discrete Applied Mathematics 31, 261–277 (1991)
Gladkiĭ, A.V.: On the complexity of derivations in phase-structure grammars. Algebra i Logika Seminar 3(5-6), 29–44 (1964) (in Russian)
Head, T.: Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors. Bulletin of Mathematical Biology 49, 737–759 (1987)
Hartmanis, J., Mahaney, S.R.: Languages simultaneously complete for one-way and two-way log-tape automata. SIAM Journal of Computing 10(2), 383–390 (1981)
Hopcroft, J E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading, MA (1979)
Ladner, R.E., Lynch, N.A.: Relativization of questions about logspace computability. Mathematical Systems Theory 10(1), 19–32 (1976)
Ogihara, M.: Relating the minimum model for DNA computation and Boolean circuits. Proceedings of the 1999 Genetic and Evolutionary Computation Conference, pp. 1817–1821. Morgan Kaufmann Publishers, San Francisco, CA (1999)
Ogihara, M., Ray, A.: The minimum DNA computation model and its computational power. In: Ogihara, M., Ray, A. (eds.) Unconventional Models of Computation, Singapore, pp. 309–322. Springer, Heidelberg (1998)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading, MA (1994)
Păun, G.: Regular extended H systems are computationally universal. Journal of Automata, Languages, Combinatorics 1(1), 27–36 (1996)
Păun, G., Rozenberg, G., Salomaa, A.: Computing by splicing. Theoretical Computer Science 168(2), 32–336 (1996)
Păun, G., Rozenberg, G., Salomaa, A.: DNA Computing - New Computing Paradigms. Springer-Verlag, Berlin Heidelberg (1998)
Pixton, D.: Regularity of splicing languages. Discrete Applied Mathematics 69, 101–124 (1996)
Reif, J.H.: Parallel molecular computation. Proceedings of the 7th ACM Symposium on Parallel Algorithms and Architecture, pp. 213–223. ACM Press, New York (1995)
Ruzzo, W.: On uniform circuit complexity. Journal of Computer and System Sciences 22, 365–383 (1981)
Venkateswaran, H.: Properties that characterize LOGCFL. Journal of Computer and System Sciences 43, 380–404 (1991)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Loos, R., Ogihara, M. (2007). Complexity Theory for Splicing Systems. In: Harju, T., Karhumäki, J., Lepistö, A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73208-2_29
Download citation
DOI: https://doi.org/10.1007/978-3-540-73208-2_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73207-5
Online ISBN: 978-3-540-73208-2
eBook Packages: Computer ScienceComputer Science (R0)