A right act over a semigroup S is a set X with a map X × S → X, (x, s) 7→ xs satisfying (xs)s′ = x(ss′) for all x ∈ X, s, s′ ∈ S (see [1]). A left S-act Y over the semigroup S is defined analogously: S × Y → Y , (s, y) 7→ sy, s(s′y) = (ss′)y for all s, s′ ∈ S, y ∈ Y . Let S, T be semigroups. A set Z is called an (S, T )-act (bi-act over S and T), if it is a left S-act and a right T -act at the same time and (sz)t = s(zt) for all z ∈ Z, s ∈ S, t ∈ T. The right S-act X, left S-act Y and (S, T )-bi-act Z may be denoted by XS , SY , and SZT . A generating set G of the act (S × S)S is called irreducible if none of its subsets G′ ⊂ G is a generating set of this act. Clearly, any finite generating set may be reduced to an irreducible one. A generating set is called minimal if it is minimal with respect to power. Note that a diagonal act over a semigroup is a unary algebra. Indeed, if S is a semigroup, then multiplication by s ∈ S may be thought as applying unary operation φs : x 7→ xs, where x ∈ S. Therefore, the following theorem is applicable to diagonal acts.