A Thirty Year Old Conjecture about Promise Problems

  • Andrew Hughes
  • A. Pavan
  • Nathan Russell
  • Alan Selman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7391)


Even, Selman, and Yacobi [ESY84, SY82] formulated a conjecture that in current terminology asserts that there do not exist disjoint NP-pairs all of whose separators are NP-hard viaTuring reductions. In this paper we consider a variant of this conjecture—there do not exist disjoint NP-pairs all of whose separators are NP-hard via bounded-truth-table reductions. We provide evidence for this conjecture. We also observe that if the original conjecture holds, then some of the known probabilistic public-key cryptosystems are not NP-hard to crack.


Proof System Satisfying Assignment Homomorphic Encryption Reasonable Hypothesis Promise Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andrew Hughes
    • 1
  • A. Pavan
    • 2
  • Nathan Russell
    • 1
  • Alan Selman
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity at BuffaloUSA
  2. 2.Department of Computer ScienceIowa State UniversityUSA

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