Construction of rational expression from tree automata using a generalization of Arden's Lemma

Arden's Lemma is a classical result in language theory allowing the computation of a rational expression denoting the language recognized by a finite string automaton. In this paper we generalize this important lemma to the rational tree languages. Moreover, we propose also a construction of a rational tree expression which denotes the accepted tree language of a finite tree automaton

Tree pattern matching from regular tree expressions

summary:In this work we deal with tree pattern matching over ranked trees, where the pattern set to be matched against is defined by a regular tree expression. We present a new method that uses a tree automaton constructed inductively from a regular tree expression. First we construct a special tree automaton for the regular tree expression of the pattern $E$, which is somehow a generalization of Thompson automaton for strings. Then we run the constructed automaton on the subject tree $t$. The pattern matching algorithm requires an $\mathcal{O}(\vert t\vert\vert E\vert)$ time complexity, where $\vert t\vert$ is the number of nodes of $t$ and $\vert E\vert$ is the size of the regular tree expression $E$. The novelty of this contribution besides the low time complexity is that the set of patterns can be infinite, since we use regular tree expressions to represent patterns