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.
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Hughes, A., Mandal, D., Pavan, A. et al. A thirty Year old conjecture about promise problems. comput. complex. 25, 883–919 (2016). https://doi.org/10.1007/s00037-015-0107-6
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DOI: https://doi.org/10.1007/s00037-015-0107-6