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arXiv · 1902.00812

Planar digraphs for automatic complexity

Achilles A. Beros·Bjørn Kjos-Hanssen·Daylan Kaui Yogi
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Abstract

We show that the digraph of a nondeterministic finite automaton witnessing the automatic complexity of a word can always be taken to be planar. In the case of total transition functions studied by Shallit and Wang, planarity can fail. Let $s_q(n)$ be the number of binary words $x$ of length $n$ having nondeterministic automatic complexity $A_N(x)=q$. We show that $s_q$ is eventually constant for each $q$ and that the eventual constant value of $s_q$ is computable.

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Achilles A. Beros, Bjørn Kjos-Hanssen, Daylan Kaui Yogi. 2019-02-02. Planar digraphs for automatic complexity. https://arxiv.org/abs/1902.00812

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