Planar Digraphs for Automatic Complexity

  • Achilles A. Beros
  • Bjørn Kjos-HanssenEmail author
  • Daylan Kaui Yogi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11436)


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.


Automatic complexity Planar graph Möbius function Nondeterministic finite automata 


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Authors and Affiliations

  1. 1.University of Hawai‘i at MānoaHonoluluUSA

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