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We study the generic properties of finitely presented monoids and semigroups.We show that for positive integers a > 1, k and m, the generic a-generatork-relation monoid and semigroup presentation (defined in any of severaldefinite statistical senses) satisfy the small overlap condition C(m). Itfollows that the generic monoid is torsion-free and J-trivial and, by a recentresult of the author, admits a linear time solution to its word problem and aregular language of unique normal forms for its elements. Moreover, the uniformword problem for finitely presented monoids is generically solvable in timelinear in the word lengths and quadratic in the presentation size. We alsoprove some technical results about generic sets which may be of independentinterest.

On generic properties of finitely presented monoids and semigroups