Showing 1–1 of 1 results for author: Du, C F

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

Authors: Chen Fei Du, Hamoon Mousavi, Luke Schaeffer, Jeffrey Shallit

Abstract: 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… ▽ More 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 application of our method we prove a new result: there exists an aperiodic infinite binary word avoiding the pattern x x x^R. This is the first avoidability result concerning a nonuniform morphism proven purely mechanically. △ Less

Submitted 27 July, 2014; v1 submitted 3 June, 2014; originally announced June 2014.

Comments: inserted new section 9 on abelian properties