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.
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