No abstract

Abstract. Champarnaud and Ziadi, and Khorsi et al. show how to compute the equation automaton of word regular expression E via the k-CContinuations. Kuske and Meinecke extend the computation of the equation automaton to a regular tree expression E over a ranked alphabet Σ and produce a O(R · | E | 2 ) time and space complexity algorithm, where R is the maximal rank of a symbol occurring in Σ and | E | is the size of E. In this paper, we give a full description of the algorithm based on the acyclic minimization of Revuz. Our algorithm, which is performed in an O(|Q| · | E |) time and space complexity, where |Q| is the number of states of the produced automaton, is more efficient than the one obtained by Kuske and Meinecke.

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.

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 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 c-continuation tree automaton C, we show that the previous morphic relations are still valid on tree expressions.