Some Reducibilities on Regular Sets
We discuss some known and introduce some new reducibilities on regular sets. We establish some facts on the corresponding degree structures and relate some reducibilities to natural hierarchies of regular sets. As an application, we characterize regular languages whose leaf-language classes (in the balanced model) are contained in the polynomial hierarchy. For any reducibility we try to give some motivation and interesting open questions, in a hope to convince the reader that study of these reducibilities is important for automata theory and computational complexity.
KeywordsRegular Language Automaton Theory Interesting Open Question Degree Structure Natural Hierarchy
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- 7.Hertrampf, U., Lautemann, C., Schwentick, T., Vollmer, H., Wagner, K.W.: On the power of polynomial time bit-reductions. Proc. 8th Structure in Complexity Theory, 200–207 (1993)Google Scholar
- 8.Immermann, N.: Descriptive Complexity. Springer, Berlin (1999)Google Scholar
- 13.Selivanov, V.L.: Some hierarchies and reducibilities on regular languages. University of Würzburg, Technical Report 349, 21 (2004)Google Scholar
- 14.Shukin, A.G.: Difference hierarchies of regular languages. Comp. Systems, Novosibirsk 161, 141–155 (1998) (in Russian)Google Scholar
- 15.Selivanov, V.L., Shukin, A.G.: On hierarchies of regular star-free languages (in Russian). Preprint 69 of A.P. Ershov Institute of Informatics Systems, p. 28 (2000)Google Scholar
- 19.Vereshchagin, N.K.: Relativizable and non-relativizable theorems in the polynomial theory of algorithms. Izvestiya Rossiiskoi Akademii Nauk 57, 51–90 (1993) (in Russian, there is English translation)Google Scholar