Abstract
Karp and Lipton introduced advice-taking Turing machines to capture nonuniform complexity classes. We study this concept for automata-like models and compare it to other nonuniform models studied in connection with formal languages in the literature. Based on this we obtain complete separations of the classes of the Chomsky hierarchy relative to advices.
Part of the work done while the author worked at Institut für Informatik, Technische Universität München, Arcisstr. 21, D-80290 München, Germany.
Preview
Unable to display preview. Download preview PDF.
References
R. Aleliunas, R. M. Karp, R. J. Lipton, L. Lovasz, and C. Rackoff. Random walks, universal traversal sequences, and the complexity of MAZE problems. In Proceedings of the 20th IEEE Annual Symposium on Foundations of Computer Science, pages 218–223, 1979.
J. L. Balcázar, J. Díaz, and J. Gabarró. Uniform characterizations of non-uniform complexity measures. Information and Control, 67:53–69, 1985.
C. Damm and M. Holzer. Inductive counting below LOGSPACE. In Proceedings of the 19th Conference on Mathematical Foundations of Computer Science, number 841 in LNCS, pages 276–285. Springer, August 1994.
G. Goodrich, R. Ladner, and M. Fischer. Straight line programs to compute finite languages. In Conference on Theoretical Computer Science, Waterloo, 1977.
R. L. Graham, B. L. Rothschild, and J. H. Spencer. Ramsey theory. Wiley, 1990.
D. T. Huynh. Complexity of closeness, sparseness and segment equivalence for context-free and regular languages. In Informatik, Festschrift zum 60. Geburtstag von Günter Hotz, pages 235–251. B. G. Teubner, 1992.
O. H. Ibarra and B. Ravikumar. Sublogarithmic-space Turing machines, nonuniform space complexity, and closure properties. Mathematical Systems Theory, 21:1–17, 1988.
R. M. Karp and R. J. Lipton. Turing machines that take advice. L'Enseignement Mathématique, 28:191–209, 1982.
M. Li and P. Vitányi. An Introduction to Kolmogorov Complexity and its Applications. Springer, New York, Berlin, Heidelberg, 1993.
M. Mundhenk and R. Schuler. Random languages for nonuniform complexity classes. Journal of Complexity, 7:296–310, 1991.
N. Pippenger. On simultaneous resource bounds. In Proceedings of the 20th IEEE Annual Symposium on Foundations of Computer Science, pages 307–311, 1979.
J. Shallit and Y. Breitbart. Automaticity: properties of a measure of descriptional complexity. In Annual Symposium on Theoretical Aspects of Computing, number 775 in Lecture Notes in Computer Science, pages 619–630. Springer, 1994.
A. Wigderson. NL/poly ⊂⊕L/poly. In Proceedings of the 9th Annual Structure in Complexity Theory Conference, pages 59–62, Juni 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Damm, C., Holzer, M. (1995). Automata that take advice. In: Wiedermann, J., Hájek, P. (eds) Mathematical Foundations of Computer Science 1995. MFCS 1995. Lecture Notes in Computer Science, vol 969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60246-1_121
Download citation
DOI: https://doi.org/10.1007/3-540-60246-1_121
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60246-0
Online ISBN: 978-3-540-44768-9
eBook Packages: Springer Book Archive