An Efficient Algorithm for the Construction of the Equation Tree Automaton

Abstract

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.