Abstract
In this paper, we consider the problem of what topological semigroups can serve as input semigroups of what (topological) automata. A semigroup is said to be admissible if it serves as an input semigroup of a non-trivial “strongly connected” automaton that has a distinguishable state (see Definition 2). For the discrete or the compact case, the class of all the admissible semigroups is fully characterized: a discrete or compact topological semigroup (I, m) is admissible if and only if there exists a closed congruence relationR such that the quotient semigroup (I/R, m R ) is non-trivial, right simple, and left unital. This work stems from Weeg's [10], who considered a similar problem in the discrete case.
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