RAIRO-Theor. Inf. Appl.
Volume 50, Number 1, January-March 2016Special issue dedicated to the 15th "Journées Montoises d'Informatique Théorique"
|Page(s)||39 - 66|
|Published online||02 June 2016|
Decision algorithms for Fibonacci-automatic Words, I: Basic results
School of Computer Science, University of Waterloo,
2 Computer Science and Artificial Intelligence Laboratory, The Stata Center, MIT Building 32, 32 Vassar Street, Cambridge, MA 02139, USA
Received: 24 March 2016
Accepted: 29 March 2016
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 = f0f1f2··· = 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.
Mathematics Subject Classification: 11B85 / 68R15 / 11A67 / 11B39 / 03D05 / 68Q45
Key words: Decision procedure / infinite word / Fibonacci-automatic – square / cube / palindrome / first-order logic / Fibonacci representation – quasiperiod / unbordered word / Lyndon word / uniform recurrence – linear recurrence / critical exponent
© EDP Sciences 2016
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