Monoidal Finite-State Automaton
A monoidal finite-state automaton (MSA) is a tuple of the form \(A = (\mathit{M}, \mathit{Q}, \mathit{I}, \mathit{F}, \Delta)\) where:
- \(\mathit{M} = (\texttt{M}, \circ, 1)\) is a Monoid.
- \(\mathit{Q}\) is a finite set of states.
- \(\mathit{I} \subseteq \mathit{Q}\) is the set of initial states.
- \(\mathit{F} \subseteq \mathit{Q}\) is the set of final states.
- \(\Delta \subseteq \mathit{Q} \times \texttt{M} \times \mathit{Q}\) is a finite set called transition relation.