Semiautomaton

A semiautomaton is a stripped-down Deterministic Finite Automaton that only has a transition relation. Explicitly, a semiautomaton on an alphabet $\Sigma$ consists of a set of states $Q$, and a transition function $\Sigma\times Q\to Q$.

As algebras

A semiautomaton is a Functor Algebra for the functor $\Sigma\times-:\mathrm{Sets}{.}\to\mathrm{Sets}{.}$.

References

• https://en.wikipedia.org/wiki/Semiautomaton