Generic complexity of first-order theories

Theory of generic complexity studies algorithmical problems for “almost all” inputs. A problem can be hard or undecidable in the worst case but feasible in the generic case. In this review we describe some recent results about generic complexity of the following first order theories: any undecidable first order theory (Mysnikov, Rybalov), ordered field of real numbers (Rybalov, Fedosov), Presburger arithmetic (Rybalov).