Some Combinatorial Operators in Language Theory

Multitildes are regular operators that were introduced by Caron et al. in order to increase the number of Glushkov automata. In this paper, we study the family of the multitilde operators from an algebraic point of view using the notion of operad. This leads to a combinatorial description of already known results as well as new results on compositions, actions and enumerations.Comment: 21 page

Acyclic automata and small expressions using multi-tilde-bar operators

AbstractA regular expression with n occurrences of symbol can be converted into an equivalent automaton with (n+1) states, the so-called Glushkov automaton of the expression. Conversely, it is possible to decide whether a given (n+1)-state automaton is a Glushkov one and, if so, to convert it back to an equivalent regular expression of width n. Our goal is to extend the class of automata for which such a linear retranslation is possible. We define new regular operators, called multi-tilde-bars, allowing us to simultaneously apply a multi-tilde operator and a multi-bar one to a list of expressions. The main results are that a multi-tilde-bar expression of width n can be converted into an (n+1)-state position-like automaton and that any acyclic n-state automaton can be turned into an extended expression of width O(n)