Paper The following article is Open access

Generic NP-incomplete problems

Published under licence by IOP Publishing Ltd
, , Citation Alexander Rybalov 2018 J. Phys.: Conf. Ser. 1050 012072 DOI 10.1088/1742-6596/1050/1/012072

1742-6596/1050/1/012072

Abstract

Ladner in 1975 proved that if P ≠ NP then there exist problems in NP, which are not decidable in polynomial time and not NP-complete. Kapovich, Myasnikov, Schupp and Shpilrain in 2003 developed a theory of generic-case complexity. Generic-case approach considers an algorithmic problem on "most" of inputs instead of all domain and ignores its behaviour on the rest of inputs. In this paper we prove a generic analog of the Ladner's theorem: If P ≠ NP and P = BPP, then there exists a set S ∈ NP, such that S is not strongly generically decidable in polynomial time and not generically NP-complete. Supported by Russian Science Foundation, grant 17-11-01117.

Export citation and abstract BibTeX RIS

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Please wait… references are loading.
10.1088/1742-6596/1050/1/012072