computational complexity

, Volume 25, Issue 4, pp 883–919 | Cite as

A thirty Year old conjecture about promise problems

  • Andrew Hughes
  • Debasis Mandal
  • A. Pavan
  • Nathan Russell
  • Alan L. Selman
Article

Abstract

Even, Selman, and Yacobi (Even et al. in Inf Control 61(2):159–173, 1984, Selman and Yacobi in Proceedings of the 8th international colloquium on automata, languages, and programming, volume 140 of lecture notes in computer science. Springer, Berlin, pp 502–509, 1982) formulated a conjecture that in current terminology asserts that there do not exist disjoint NP-pairs all of whose separators are NP-hard via Turing 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.

Keywords

Promise problems ESY conjecture NP completeness truth-table reductions public-key cryptosystems 

Subject Classification

68Q15 68Q17 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Andrew Hughes
    • 1
  • Debasis Mandal
    • 2
  • A. Pavan
    • 2
  • Nathan Russell
    • 1
  • Alan L. Selman
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity at Buffalo, SUNYBuffaloUSA
  2. 2.Department of Computer ScienceIowa State UniversityAmesUSA

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