Constructing Embeddings and Isomorphisms of Finite Abstract Semigroups
  We present a search algorithm for constructing embeddings and deciding isomorphisms of semigroups, working with their multiplication tables. The algorithm is used for enumerating diagram semigroups up to isomorphism and for finding minimal degree representations. 
James East, Attila Egri-Nagy, Andrew R. Francis, James D. Mitchell
math.GR