Automata Theory, Classification by semi-groups

A mathematically significant classification of transducers may be obtained in terms of the theory of semi-groups. In outline, if the transducer T is reduced, the functions fs given in terms of M, for fixed input, as maps from and to the space of states Q constitute a semi-group termed the semi-group of T (see 14). By a certain procedure these semi-groups and their associated transducers