What is "semiautomaton"

n. (context mathematics computer science English) a multiplicative operation of a monoid on a set

In mathematics and theoretical computer science, a semiautomaton is a deterministic finite automaton having inputs but no output. It consists of a set Q of states, a set Σ called the input alphabet, and a function T: Q × Σ → Q called the transition function.

Associated to any semiautomaton is a monoid called the characteristic monoid, input monoid, transition monoid or transition system of the semiautomaton, which acts on the set of states Q. This may be viewed either as an action of the free monoid of strings in the input alphabet Σ, or as the induced transformation semigroup of Q.

In older books like Clifford and Preston (1967) S-acts are called "operands".

In category theory, semiautomata essentially are functors.