Abstract
Assume that \(\text{NP}\not\subset\text{BPP}\). Gutfreund, Shaltiel, and Ta-Shma in [Computational Complexity 16(4):412-441 (2007)] have proved that for every randomized polynomial time decision algorithm D for SAT there is a polynomial time samplable distribution such that D errs with probability at least 1/6 − ε on a random formula chosen with respect to that distribution. A challenging problem is to increase the error probability to the maximal possible 1/2 − ε (the random guessing has success probability 1/2). In this paper, we make a small step towards this goal: we show how to increase the error probability to 1/3 − ε.
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
Bogdanov, A., Trevisan, L.: Average-Case Complexity. Foundations and Trends in Theoretical Computer Science 1(2), 1–106 (2006)
Leonid, A.: Levin, Average Case Complete Problems. SIAM J. Comput. 15(1), 285–286 (1986)
Ben-David, S., Chor, B., Luby, O.G.M.: On the Theory of Average Case Complexity. In: STOC, pp. 204–216 (1989)
Gutfreund, D.: Worst-Case Vs. Algorithmic Average-Case Complexity in the Polynomial-Time Hierarchy. In: Díaz, J., Jansen, K., Rolim, J.D.P., Zwick, U. (eds.) APPROX 2006 and RANDOM 2006. LNCS, vol. 4110, pp. 386–397. Springer, Heidelberg (2006)
Bogdanov, A., Talwar, K., Wan, A.: Hard instances for satisfiability and quasi-one-way functions. In: Proceedings of Innovations in Computer Science (ICS 2009), pp. 290–300. Tsinghua University Press (2009)
Gutfreund, D., Shaltiel, R., Ta-Shma, A.: If NP Languages are Hard on the Worst-Case, Then it is Easy to Find Their Hard Instances. Computational Complexity (CC) 16(4), 412–441 (2007)
Adleman, L.M.: Two Theorems on Random Polynomial Time. In: FOCS 1978, pp. 75–83 (1978)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vereshchagin, N. (2013). Improving on Gutfreund, Shaltiel,and Ta-Shma’s Paper “If NP Languages Are Hard on the Worst-Case, Then It Is Easy to Find Their Hard Instances”. In: Bulatov, A.A., Shur, A.M. (eds) Computer Science – Theory and Applications. CSR 2013. Lecture Notes in Computer Science, vol 7913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38536-0_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-38536-0_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38535-3
Online ISBN: 978-3-642-38536-0
eBook Packages: Computer ScienceComputer Science (R0)