Abstract
Generic approach is one of the approaches to the study of algorithmic problems for almost all inputs, born at the intersection of computational algebra and computer science. Within the framework of this approach, algorithms are studied that solve a problem for almost all inputs, and for the remaining rare inputs give an undefined answer. This review reflects two areas of research of generic complexity of algorithmic problems in algebra, mathematical logic, number theory, and theoretical computer science. The first direction is devoted to the construction of generic algorithms for problems that are unsolvable and hard in the classical sense. In the second direction, algorithmic problems are sought that remain unsolvable or hard even in the generic sense. Such problems are important in cryptography.
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