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Decidability of Krohn-Rhodes Complexity for Finite Semigroups

The result, settling a problem open for over fifty years, that the Krohn-Rhodes complexity of a finite semigroup, the least number of group factors in any wreath-product decomposition into groups and aperiodic semigroups, can be algorithmically computed from its multiplication table, together with the upper-bound, lower-bound, and structural tools that make the search over decompositions effective.