In previous papers, Krohn and Rhodes exploited the natural connection between finite semigroups and finite-state sequential machines to prove a prime decomposition theorem for finite semigroups and… (More)

# G (S) denotes the complexity of a finite semigroup as introduced by Krohn and Rhodes. IfI is a maximal ideal or maximal left ideal of a semigroupS, then# G (I) ⩽ # G (S) ⩽ # G (I) + 1. Thus, ifV is… (More)

We should like to make the following correct ions to ou r earl ier paper .* In Definition l(c) o f Section 2, p. 62, replace "YI1 C Is" by "YI~ C_ I~". In the last line o f Proposi t ion 2 o f… (More)

In an earlier paper, Maurer and Rhodes (1965) proved the following result: Let G be a finite simple nonabelian group and f: G" --> G a map of the set of n-tuples of elements of G into G. Then there… (More)

Herein we obtain several theoretical results concerning properties of the transition hmction giverL by a finite net of threshold elements. In particular, we are able to give an exact characterization… (More)