Bottom Up Quotients and Residuals for Tree Languages
Formal Languages and Automata Theory
2015-06-10 v1
Abstract
In this paper, we extend the notion of tree language quotients to bottom-up quotients. Instead of computing the residual of a tree language from top to bottom and producing a list of tree languages, we show how to compute a set of k-ary trees, where k is an arbitrary integer. We define the quotient formula for different combinations of tree languages: union, symbol products, compositions, iterated symbol products and iterated composition. These computations lead to the definition of the bottom-up quotient tree automaton, that turns out to be the minimal deterministic tree automaton associated with a regular tree language in the case of the 0-ary trees.
Keywords
Cite
@article{arxiv.1506.02863,
title = {Bottom Up Quotients and Residuals for Tree Languages},
author = {Jean-Marc Champarnaud and Ludovic Mignot and Nadia Ouali-Sebti and Djelloul Ziadi},
journal= {arXiv preprint arXiv:1506.02863},
year = {2015}
}