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Tree automata constructions from regular expressions: a comparative study. (English) Zbl 1386.68095
Summary: 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 \(\mathcal{P}\) due to Glushkov, the c-continuation automaton \(\mathcal{C}\) due to Champarnaud and Ziadi, the follow automaton \(\mathcal F\) due to Ilie and Yu and the equation automaton \(\mathcal{E}\) due to Antimirov. It has been shown that \(\mathcal P\) and \(\mathcal C\) are isomorphic and that \(\mathcal E\) (resp. \(\mathcal F\)) is a quotient of \(\mathcal C\) (resp. of \(\mathcal P\)).
In this paper, we define from a given regular tree expressionthe position tree automaton \(\mathcal P\) and the follow tree automaton \(\mathcal F\). Using the definition of the equation tree automaton \(\mathcal E\) of Kuske and Meinecke and our previously defined c-continuation tree automaton \(\mathcal C\), we show that the previous morphic relations are still valid on tree expressions.
68Q45 Formal languages and automata
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