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arXiv · 1910.02164

Unambiguous separators for tropical tree automata

Thomas Colcombet·Sylvain Lombardy
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Abstract

In this paper we show that given a max-plus automaton (over trees, and with real weights) computing a function $f$ and a min-plus automaton (similar) computing a function $g$ such that $f\leqslant g$, there exists effectively an unambiguous tropical automaton computing $h$ such that $f\leqslant h\leqslant g$. This generalizes a result of Lombardy and Mairesse of 2006 stating that series which are both max-plus and min-plus rational are unambiguous. This generalization goes in two directions: trees are considered instead of words, and separation is established instead of characterization (separation implies characterization). The techniques in the two proofs are very different.

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Thomas Colcombet, Sylvain Lombardy. 2019-10-04. Unambiguous separators for tropical tree automata. https://arxiv.org/abs/1910.02164

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