Decision Algorithms for Fibonacci-Automatic Words, with Applications to Pattern Avoidance

@article{Du2014DecisionAF,
title={Decision Algorithms for Fibonacci-Automatic Words, with Applications to Pattern Avoidance},
author={Chen Fei Du and Hamoon Mousavi and Luke Schaeffer and Jeffrey Shallit},
journal={CoRR},
year={2014},
volume={abs/1406.0670}
}

We implement a decision procedure for answering questions about a class of infinite words that might be called (for lack of a better name) “Fibonacci-automatic”. This class includes, for example, the famous Fibonacci word f = 01001010 · · · , the fixed point of the morphism 0→ 01 and 1→ 0. We then recover many results about the Fibonacci word from the literature (and improve some of them), such as assertions about the occurrences in f of squares, cubes, palindromes, and so forth. As an… CONTINUE READING