There exist several methods of computing an automaton recognizing the language denoted by a given regular expression: In the case of words, the position automaton 𝒫 due to Glushkov, the c-continuation automaton 𝒞 due to Champarnaud and Ziadi, the follow automaton ℱ due to Ilie and Yu and the equation automaton ɛ due to Antimirov. It has been shown that 𝒫 and 𝒞 are isomorphic and that ɛ (resp. ℱ) is a quotient of 𝒞 (resp. of 𝒫). In this paper, we define from a given regular tree expression the position tree automaton 𝒫 and the follow tree automaton ℱ. Using the definition of the equation tree automaton ɛ of Kuske and Meinecke and our previously defined c-continuation tree automaton 𝒞, we show that the previous morphic relations are still valid on tree expressions.

This paper proposes an extension to classical regular expressions by the addition of two operators allowing the inclusion of boolean formulae from the zeroth order logic. These expressions are called constrained expressions. The associated language is defined thanks to the notion of interpretation and of realization. We show that the language associated when both interpretation and realization are fixed is stricly regular and can be not regular otherwise. Furthermore, we use an extension of Antimirov’s partial derivatives in order to solve the membership test in the general case. Finally, we show that once the interpretation is fixed, the membership test of a word in the language denoted by a constrained expression can be undecidable whereas it is always decidable when the interpretation is not fixed.

The aim of this paper is to design a polynomial construction of a finite recognizer for hairpin completions of regular languages. This is achieved by considering completions as new expression operators and by applying derivation techniques to the ass