Complexity with Rod

  • Lance FortnowEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10010)


Rod Downey and I have had a fruitful relationship though direct and indirect collaboration. I explore two research directions, the limitations of distillation and instance compression, and whether or not we can create NP-incomplete problems without punching holes in NP-complete problems.


Instance Compression Indirect Collaboration Rahul Santhanam Honest Reductions Distillation Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I’d like to thank the anonymous referee for several helpful comments.


  1. 1.
    Downey, R., Fortnow, L.: Uniformly hard languages. Theor. Comput. Sci. 298(2), 303–315 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Fortnow, L.: Kolmogorov complexity. In: Downey, R., Hirschfeldt, D. (eds.) Aspects of Complexity, Minicourses in Algorithmics, Complexity, and Computational Algebra, NZMRI Mathematics Summer Meeting. de Gruyter Series in Logic and Its Applications, Kaikoura, New Zealand, 7–15 January 2000, vol. 4. de Gruyter (2001)Google Scholar
  3. 3.
    Downey, R., Hirschfeldt, D.: Algorithmic Randomness and Complexity. Springer Science & Business Media, Heidelberg (2010)CrossRefzbMATHGoogle Scholar
  4. 4.
    Fortnow, L., Santhanam, R.: Infeasibility of instance compression and succinct PCPs for NP. J. Comput. Syst. Sci. 77(1), 91–106 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bodlaender, H., Downey, R., Fellows, M., Hermelin, D.: On problems without polynomial kernels. J. Comput. Syst. Sci. 75(8), 423–434 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Harnik, D., Naor, M.: On the compressibility of NP instances and cryptographic applications. SIAM J. Comput. 39(5), 1667–1713 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Buhrman, H., Hitchcock, J.: NP-hard sets are exponentially dense unless coNP is contained in NP/poly. In: 23rd Annual IEEE Conference on Computational Complexity, CCC 2008, pp. 1–7. IEEE, New York, June 2008Google Scholar
  8. 8.
    Drucker, A.: New limits to classical and quantum instance compression. SIAM J. Comput. 44(5), 1443–1479 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Post, E.: Recursively enumerable sets of positive integers and their decision problems. Bullet. Am. Math. Soc. 50(5), 284–316 (1944)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Soare, R.: Recursively Enumerable Sets and Degrees. Springer, Berlin (1987)CrossRefzbMATHGoogle Scholar
  11. 11.
    Cook, S.: The complexity of theorem-proving procedures. In: Proceedings of the 3rd ACM Symposium on the Theory of Computing, pp. 151–158. ACM, New York (1971)Google Scholar
  12. 12.
    Karp, R.: Reducibility among combinatorial problems. In: Miller, R., Thatcher, J. (eds.) Complexity of Computer Computations. The IBM Research Symposia Series, pp. 85–103. Springer, New York (1972). doi: 10.1007/978-1-4684-2001-2_9 CrossRefGoogle Scholar
  13. 13.
    Ladner, R.: On the structure of polynomial time reducibility. J. ACM 22, 155–171 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Fortnow, L., Santhanam, R.: Robust Simulations and Significant Separations, pp. 569–580. Springer, Heidelberg (2011)zbMATHGoogle Scholar
  15. 15.
    Fortnow, L., Santhanam, R.: New non-uniform lower bounds for uniform classes. In: Raz, R. (ed.) 31st Conference on Computational Complexity (CCC 2016). Leibniz International Proceedings in Informatics (LIPIcs), vol. 50, pp. 19:1–19:14. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany (2016)Google Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Georgia Institute of TechnologyAtlantaUSA

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