On generic NP-completeness of the Boolean satisfiability problem

Generic-case approach to algorithmic problems was suggested by Miasnikov, Kapovich, Schupp and Shpilrain in 2003. This approach studies behavior of an algorithm on typical (almost all) inputs and ignores the rest of inputs. Many classical undecidable or hard algorithmic problems become feasible in the generic case. But there are generically hard problems. In this paper we introduce a notion of generic polynomial reducibility algorithmic problems, which preserve the property of polynomial decidability of the problem for almost all inputs and has the property of transitivity. It is proved that the classical satisfiability problem of Boolean formulas is complete with respect to this generic reducibility in the generic analogue of class NP.