Abstract
Building on Barak’s work (Random’02), Fortnow and Santhanam (FOCS’04) proved a time hierarchy for probabilistic machines with one bit of advice. Their argument is based on an implicit translation technique, which allow to translate separation results for short (say logarithmic) advice (as shown by Barak) into separations for a single-bit advice. In this note, we make this technique explicit, by introducing an adequate translation lemma.
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
Barak, B.: A Probabilistic-Time Hierarchy Theorem for Slightly Non-uniform Algorithms. In: Rolim, J.D.P., Vadhan, S.P. (eds.) RANDOM 2002. LNCS, vol. 2483, pp. 194–208. Springer, Heidelberg (2002)
Fortnow, L., Santhanam, R.: Hierarchy theorems for probabilistic polynomial time. In: 45th FOCS, pp. 316–324 (2004)
van Melkebeek, D., Pervyshev, K.: A Generic Time Hierarchy for Semantic Models with One Bit of Advice. Computational Complexity 16, 139–179 (2007)
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Goldreich, O., Sudan, M., Trevisan, L. (2011). From Logarithmic Advice to Single-Bit Advice. In: Goldreich, O. (eds) Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation. Lecture Notes in Computer Science, vol 6650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22670-0_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-22670-0_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22669-4
Online ISBN: 978-3-642-22670-0
eBook Packages: Computer ScienceComputer Science (R0)