A generic algorithm for the membership problem in the semigroups of integer matrices

Abstract

Generic-case approach to algorithmic problems was suggested by A. Miasnikov, I. Kapovich, P. Schupp and V. Shpilrain in 2003. This approach studies behavior of an algorithm on typical (almost all) inputs and ignores the rest of inputs. In this paper we prove generic decidability of the membership problem and the mortality problem for semigroups of integer matrices of arbitrary order.