An algebraic representation of the fixed-point closure of *-continuous Kleene algebras – A categorical Chomsky–Schützenberger theorem

Abstract The family ${\mathcal{R}} X^*$ of regular subsets the free monoid $X^*$ generated by a finite set X is standard example ${}^*$ -continuous Kleene algebra. Likewise, ${\mathcal{C}} context-free $\mu$ Chomsky algebra, i.e. an idempotent semiring that closed under well-behaved least fixed-point operator . For arbitrary monoids M , M$ closure ${\mathcal{R}}M$ as more briefly, We provide algebraic representation in suitable product with $C_2'$ quotient sets over alphabet $\Delta_2$ two pairs bracket symbols. Namely, ${\mathcal{C}}M$ isomorphic to centralizer those elements commute all This generalizes well-known result and Schützenberger (1963, Computer Programming Formal Systems 118–161) admits us denote languages $X\subseteq expressions $X\cup\Delta_2$ interpreted More generally, for any algebra K can be represented algebraically