On the State Complexity of Combined Operations
The state complexity of combined operations is studied. We show that the state complexity of a combined operation can be very different from the composition of the state complexities of the participating individual operations. However, the estimate through individual nondeterministic state complexities for each of the combined operations being considered is very similar to the actual state complexity. Several open problems related to state complexity are also proposed.
KeywordsState Complexity Regular Language Combine Operation Input Symbol Descriptional Complexity
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- 4.Campeanu, C., Salomaa, K., Yu, S.: State Complexity of Regular Languages: Finite Versus Infinite. In: Calude, C., Paun, G. (eds.) Finite vs Infinite – Contributions to an Eternal Dilemma, Ch.5, pp. 53–73. Springer, Heidelberg (2000)Google Scholar
- 6.Ellul, K., Krawetz, B., Shallit, J., Wang, M.-W.: Regular Expressions: New Results and Open Problems. Journal of Automata, Languages and Combinatorics (to appear)Google Scholar
- 7.Gao, Y., Salomaa, K., Yu, S.: State complexity of catenation and reversal combined with star. In: Descriptional Complexity of Formal Systems (DCFS 2006) (to appear)Google Scholar
- 13.Jirásková, G.: State complexity of some operations on regular languages. In: Proceedings of 5th Workshop on Descriptional Complexity of Formal Systems, pp. 114–125 (2003)Google Scholar
- 14.Jirásková, G.: State complexity of some operations on binary regular languages. Theoretical Computer Science (to appear)Google Scholar
- 16.Jirásková, G., Okhotin, A.: State complexity of cyclic shift. In: Proceedings of DCFS 2005, Como, Italy, pp. 182–193 (June 30 - July 2, 2005)Google Scholar
- 22.Salomaa, A., Salomaa, K., Yu, S.: State Complexity of Combined Operations. Theoretical Computer Science (to appear)Google Scholar
- 25.Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, pp. 41–110. Springer, Heidelberg (1997)Google Scholar
- 27.Yu, S.: State Complexity: Recent Results and Open Problems. In: ICALP 2004 Formal Language Workshop, also appears in Fundamenta Informaticae 64(1-4), 471–480 (2005) (invited talk)Google Scholar