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Given a regular language L, we effectively construct a unary semigroup that recognizes the topological closure of L in the free unary semigroup relative to the variety of unary semigroups generated by the pseudovariety R of all finite R-trivial semigroups. In particular, we obtain a new effective solution of the separation problem of regular languages by R-languages.
Motivated by the question of which completely regular semigroups have context-free word problem, we show that for certain classes of languages $mathfrak{C}$(including context-free), every completely regular semigroup that is a union of finitely many
This paper considers the word problem for free inverse monoids of finite rank from a language theory perspective. It is shown that no free inverse monoid has context-free word problem; that the word problem of the free inverse monoid of rank $1$ is b
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension complexity of fo
Let $m$ be a positive integer and let $Omega$ be a finite set. The $m$-closure of $Gle$Sym$(Omega)$ is the largest permutation group on $Omega$ having the same orbits as $G$ in its induced action on the Cartesian product $Omega^m$. The exact formula
Let $hat{F}$ be a free pro-$p$ non-abelian group, and let $Delta$ be a commutative Noetherian complete local ring with a maximal ideal $I$ such that $textrm{char}(Delta/I)=p>0$. In [Zu], Zubkov showed that when $p eq2$, the pro-$p$ congruence subgrou