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arXiv · 1506.02863

Bottom Up Quotients and Residuals for Tree Languages

Jean-Marc Champarnaud·Ludovic Mignot·Nadia Ouali-Sebti·Djelloul Ziadi
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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.

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Jean-Marc Champarnaud, Ludovic Mignot, Nadia Ouali-Sebti, Djelloul Ziadi. 2015-06-09. Bottom Up Quotients and Residuals for Tree Languages. https://arxiv.org/abs/1506.02863

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