Abstract
The reversal operation is well-studied in literature and the deterministic (respectively, nondeterministic) state complexity of reversal is known to be 2n (respectively, n). We consider the inversion operation where some substring of the given string is reversed. Formally, the inversion of a language L consists of all strings ux R v such that uxv ∈ L. We show that the nondeterministic state complexity of inversion is in Θ(n 3). We establish that the deterministic state complexity of the inversion is 2Ω(n ·logn), which is strictly worse than the worst case state complexity of the reversal operation. We also study the state complexity of different variants of the inversion operation, including prefix-, suffix-, and pseudo-inversion.
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
Birget, J.-C.: Intersection and union of regular languages and state complexity. Information Processing Letters 43(4), 185–190 (1992)
Cantone, D., Cristofaro, S., Faro, S.: Efficient string-matching allowing for non-overlapping inversions. Theoretical Computer Science 483, 85–95 (2013)
Cho, D.-J., Han, Y.-S., Kang, S.-D., Kim, H., Ko, S.-K., Salomaa, K.: Pseudo-inversion on formal languages. In: Proceeding of the 13th International Conference on Unconventional and Natural Computation (to appear)
Daley, M., Ibarra, O.H., Kari, L.: Closure and decidability properties of some language classes with respect to ciliate bio-operations. Theoretical Computer Science 306(1-3), 19–38 (2003)
Dassow, J., Mitrana, V.: Operations and language generating devices suggested by the genome evolution. Theoretical Computer Science 270(12), 701–738 (2002)
Dassow, J., Mitrana, V., Salomaa, A.: Context-free evolutionary grammars and the structural language of nucleic acids. Biosystems 43(3), 169–177 (1997)
Ésik, Z., Gao, Y., Liu, G., Yu, S.: Estimation of state complexity of combined operations. Theoretical Computer Science 410(35), 3272–3280 (2009)
Gao, Y., Salomaa, K., Yu, S.: The state complexity of two combined operations: Star of catenation and star of reversal. Fundamenta Informaticae 83(1-2), 75–89 (2008)
Holzer, M., Kutrib, M.: Nondeterministic descriptional complexity of regular languages. International Journal of Foundations of Computer Science 14(6), 1087–1102 (2003)
Holzer, M., Kutrib, M.: Descriptional and computational complexity of finite automata – a survey. Information and Computation 209, 456–470 (2011)
Kececioglu, J.D., Sankoff, D.: Exact and approximation algorithms for the inversion distance between two chromosomes. In: Apostolico, A., Crochemore, M., Galil, Z., Manber, U. (eds.) CPM 1993. LNCS, vol. 684, pp. 87–105. Springer, Heidelberg (1993)
Kutrib, M., Pighizzini, G.: Recent trends in descriptional complexity of formal languages. Bulletin of the EATCS 111, 70–86 (2013)
Lupanov, O.: A comparison of two types of finite sources. Problemy Kibernetiki 9, 328–335 (1963)
Lupski, J.R.: Genomic disorders: structural features of the genome can lead to DNA rearrangements and human disease traits. Trends in Genetics 14(10), 417–422 (1998)
Maslov, A.: Estimates of the number of states of finite automata. Soviet Mathematics Doklady 11, 1373–1375 (1970)
Meyer, A., Fisher, M.: Economy of description by automata, grammars and formal systems. In: Proceedings of the 12th Annual Symposium on Switching and Automata Theory, pp. 188–191 (1971)
Moore, F.: On the bounds for state-set size in the proofs of equivalence between deterministic, nondeterministic and two-way finite automata. IEEE Transactions on Computers C-20, 1211–1214 (1971)
Painter, T.S.: A New Method for the Study of Chromosome Rearrangements and the Plotting of Chromosome Maps. Science 78, 585–586 (1933)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Beyond Words, vol. 3. Springer-Verlag New York, Inc. (1997)
Salomaa, A., Salomaa, K., Yu, S.: State complexity of combined operations. Theoretical Computer Science 383(2-3), 140–152 (2007)
Salomaa, K., Yu, S.: On the state complexity of combined operations and their estimation. International Journal of Foundations of Computer Science 18, 683–698 (2007)
Searls, D.B.: The Computational Linguistics of Biological Sequences. In: Artificial Intelligence and Molecular Biology, pp. 47–120 (1993)
Shallit, J.: A Second Course in Formal Languages and Automata Theory, 1st edn. Cambridge University Press, New York (2008)
Vellozo, A.F., Alves, C.E.R., do Lago, A.P.: Alignment with non-overlapping inversions in O(n 3)-time. In: Bücher, P., Moret, B.M.E. (eds.) WABI 2006. LNCS (LNBI), vol. 4175, pp. 186–196. Springer, Heidelberg (2006)
Wood, D.: Theory of Computation. Harper & Row (1986)
Yokomori, T., Kobayashi, S.: DNA evolutionary linguistics and RNA structure modeling: A computational approach. In: Proceedings of INBS 1995, pp. 38–45. IEEE Computer Society (1995)
Yu, S., Zhuang, Q., Salomaa, K.: The state complexities of some basic operations on regular languages. Theoretical Computer Science 125(2), 315–328 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Cho, DJ., Han, YS., Ko, SK., Salomaa, K. (2014). State Complexity of Inversion Operations. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2014. Lecture Notes in Computer Science, vol 8614. Springer, Cham. https://doi.org/10.1007/978-3-319-09704-6_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-09704-6_10
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09703-9
Online ISBN: 978-3-319-09704-6
eBook Packages: Computer ScienceComputer Science (R0)