Abstract
We implement various oracle mechanisms on nondeterministic pushdown automata, which naturally induce nondeterministic reducibilities among formal languages in a theory of context-free languages. In particular, we examine a notion of nondeterministic many-one CFL-reducibility and carry out ground work of formulating a coherent framework for further expositions. Another more powerful reducibility—Turing CFL-reducibility—is also discussed in comparison. The Turing CFL-reducibility, in particular, makes it possible to induce a useful hierarchy (the CFL hierarchy) built over the family CFL of context-free languages. For each level of this hierarchy, basic structural properties are proven and three alternative characterizations are presented. We also show that the CFL hierarchy enjoys an upward collapse property. The first and second levels of the hierarchy are proven to be different. We argue that the CFL hierarchy coincides with a hierarchy over CFL built by applications of many-one CFL-reductions. Our goal is to provide a solid foundation for structural-complexity analyses in automata theory.
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
Berstel, J.: Transductions and Context-Free Languages. B. G. Teubner, Stuttgart (1979)
Du, D., Ko., K.: Theory of Computational Complexity. John Willey & Sons (2000)
Ginsburg, S., Greibach, S.A., Harrison, M.A.: One-way stack languages. J. ACM 14, 389–418 (1967)
Greibach, S.A.: The hardest context-free language. SIAM J. Comput. 2, 304–310 (1973)
Hromkovič, J., Schnitger, G.: On probabilistic pushdown automata. Inf. Comput. 208, 982–995 (2010)
Ladner, R., Lynch, N., Selman, A.: A comparison of polynomial-time reducibilities. Theor. Comput. Sci. 1, 103–123 (1975)
Liu, L.Y., Weiner, P.: An infinite hierarchy of intersections of context-free languages. Math. Systems Theory 7, 185–192 (1973)
Reinhardt, K.: Hierarchies over the context-free languages. In: Dassow, J., Kelemen, J. (eds.) IMYCS 1990. LNCS, vol. 464, pp. 214–224. Springer, Heidelberg (1990)
Tadaki, K., Yamakami, T., Lin, J.C.H.: Theory of one-tape linear-time Turing machines. Theor. Comput. Sci. 411, 22–43 (2010)
Yamakami, T.: Swapping lemmas for regular and context-free languages. Available at arXiv:0808.4122 (2008)
Yamakami, T.: The roles of advice to one-tape linear-time Turing machines and finite automata. Int. J. Found. Comput. Sci. 21, 941–962 (2010)
Yamakami, T.: Immunity and pseudorandomness of context-free languages. Theor. Comput. Sci. 412, 6432–6450 (2011)
Yamakami, T., Kato, Y.: The dissecting power of regular languages. Inf. Pross. Lett. 113, 116–122 (2013)
Younger, D.H.: Recognition and parsing of context-free languages in time n 3. Inf. Control 10, 189–208 (1967)
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
Yamakami, T. (2014). Oracle Pushdown Automata, Nondeterministic Reducibilities, and the Hierarchy over the Family of Context-Free Languages. In: Geffert, V., Preneel, B., Rovan, B., Štuller, J., Tjoa, A.M. (eds) SOFSEM 2014: Theory and Practice of Computer Science. SOFSEM 2014. Lecture Notes in Computer Science, vol 8327. Springer, Cham. https://doi.org/10.1007/978-3-319-04298-5_45
Download citation
DOI: https://doi.org/10.1007/978-3-319-04298-5_45
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04297-8
Online ISBN: 978-3-319-04298-5
eBook Packages: Computer ScienceComputer Science (R0)