摘要：The syntactic monoid of a language is generalized to the level of a symmetricmonoidal closed category $\mathcal D$. This allows for a uniform treatment ofseveral notions of syntactic algebras known in the literature, including thesyntactic monoids of Rabin and Scott ($\mathcal D=$ sets), the syntacticordered monoids of Pin ($\mathcal D =$ posets), the syntactic semirings ofPol\'ak ($\mathcal D=$ semilattices), and the syntactic associative algebras ofReutenauer ($\mathcal D$ = vector spaces). Assuming that $\mathcal D$ is acommutative variety of algebras or ordered algebras, we prove that thesyntactic $\mathcal D$-monoid of a language $L$ can be constructed as aquotient of a free $\mathcal D$-monoid modulo the syntactic congruence of $L$,and that it is isomorphic to the transition $\mathcal D$-monoid of the minimalautomaton for $L$ in $\mathcal D$. Furthermore, in the case where the variety$\mathcal D$ is locally finite, we characterize the regular languages asprecisely the languages with finite syntactic $\mathcal D$-monoids.
