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.
