K-Position, Follow, Equation and K-C-Continuation Tree Automata Constructions

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 E due to Antimirov. It has been shown that P and C are isomorphic and that E (resp. F) is a quotient of C (resp. of P). In this paper, we define from a given regular tree expression the k-position tree automaton P and the follow tree automaton F . Using the definition of the equation tree automaton E of Kuske and Meinecke and our previously defined k-C-continuation tree automaton C, we show that the previous morphic relations are still valid on tree expressions.