Decision algorithms for Fibonacci-automatic Words, I: Basic results
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 50 (2016) no. 1, pp. 39-66.

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=f 0 f 1 f 2 ···=01001010···, the fixed point of the morphism 001 and 10. 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.

Reçu le :
Accepté le :
DOI : 10.1051/ita/2016010
Classification : 11B85, 68R15, 11A67, 11B39, 03D05, 68Q45
Mots clés : 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
Mousavi, Hamoon 1 ; Schaeffer, Luke 2 ; Shallit, Jeffrey 1

1 School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
2 Computer Science and Artificial Intelligence Laboratory, The Stata Center, MIT Building 32, 32 Vassar Street, Cambridge, MA 02139, USA
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Mousavi, Hamoon; Schaeffer, Luke; Shallit, Jeffrey. Decision algorithms for Fibonacci-automatic Words, I: Basic results. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 50 (2016) no. 1, pp. 39-66. doi : 10.1051/ita/2016010. http://archive.numdam.org/articles/10.1051/ita/2016010/

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