The Bottom-Up Position Tree Automaton and the Father Automaton

The conversion of a given regular tree expression into a tree automaton has been widely studied. However, classical interpretations are based upon a top-down interpretation of tree automata. In this paper, we propose new constructions based on Gluskov’s one and on the one by Ilie and Yu using a bottom-up interpretation. One of the main goals of this technique is to consider as a next step the links with deterministic recognizers, something which cannot be done with classical top-down approaches.

An Efficient Algorithm for the Construction of the Equation Tree Automaton

Champarnaud et al., and Khorsi et al. show how to compute the equation automaton of a word regular expression [Formula: see text] via the C-continuations. Kuske and Meinecke extend the computation of the equation automaton to a regular tree expression [Formula: see text] over a ranked alphabet [Formula: see text] and produce a [Formula: see text] time and space complexity algorithm, where [Formula: see text] is the maximal rank of a symbol occurring in [Formula: see text] and [Formula: see text] is the size of the syntax tree of [Formula: see text]. In this paper, we give a full description of an algorithm based on the acyclic minimization of Revuz in order to compute the pseudo-continuations from the C-continuations. Our algorithm, which is performed in [Formula: see text] time and space complexity, where [Formula: see text] is the number of states of the produced automaton, is more efficient than the one obtained by Kuske and Meinecke since [Formula: see text]. Moreover, our algorithm is an output-sensitive algorithm, i.e. the complexity of which is based on the size of the produced automaton.

From Tree Automata to Rational Tree Expressions

We propose a construction of rational tree expression from finite tree automata. First, we define rational expression equation systems and we propose a substitution based method to find the unique solution. Furthermore, we discuss the case of recursion being present in an equation system, and then show under which restrictions such systems can effectively be solved. Secondly, we show that any finite tree automaton can be associated to a rational tree equation system, and that the latter can in turn be resolved. Finally, using the previous steps, a rational tree expression equivalent to the underlying automaton is extracted.