Abstract
Generic-case approach to algorithmic problems was suggested by I. Kapovich, A. Myasnikov, V. Shpilrain and P. Schupp in 2003. This approach studies behavior of an al-gorithm on typical (almost all) inputs and ignores the rest of inputs. C. Jockusch and P. Schupp in 2012 began the study of generic computability in the context of classical computability theory. In particular, they defined a generic analog of Turing reducibility. A. Rybalov in 2018 introduced a generic analog of classical m-reducibility. In this paper we study the generic m-reducibility for c.e. sets and prove that unlike classical m-reducibility, generic m-reducibility does not have the density property for c.e. sets.
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