Generic complexity of the problem of searching isomorphism of finite groupoids

The generic approach to algorithmic problems was proposed by Myasnikov, Kapovich, Schupp, and Spielrein in 2003. This approach studies the behavior of the algorithm not on the entire set of inputs, but on a certain subset (almost all) of the inputs. In this paper, we consider the general complexity of the finite groupoid isomorphism problem and prove that its natural subproblem is generically hard provided that the finite groupoid isomorphism problem is worst-case hard.