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 sq​(n) be the number of binary words x of length n having
nondeterministic automatic complexity AN​(x)=q. We show that sq​ is
eventually constant for each q and that the eventual constant value of sq​
is computable.Comment: Theory and Applications of Models of Computation (TAMC 2019), Lecture
Notes in Computer Science 11436 (2019