A thirty year old conjecture about promise problems

Authors:
Andrew Hughes;A. Pavan;Nathan Russell;Alan Selman
Affiliations:
Department of Computer Science and Engineering, University at Buffalo;Department of Computer Science, Iowa State University;Department of Computer Science and Engineering, University at Buffalo;Department of Computer Science and Engineering, University at Buffalo
Venue:
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Year:
2012

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Abstract

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.