Decision algorithms for Fibonacci-automatic Words, I: Basic results

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...

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Published inRAIRO. Informatique théorique et applications Vol. 50; no. 1; pp. 39 - 66
Main Authors Mousavi, Hamoon, Schaeffer, Luke, Shallit, Jeffrey
Format Journal Article
LanguageEnglish
Published Paris EDP Sciences 01.01.2016
Subjects
03D05
11A67
11B39
11B85
68Q45
68R15
Algorithms
critical exponent
cube
Cubes
Decision procedure
Fibonacci representation – quasiperiod
Fibonacci-automatic – square
first-order logic
infinite word
Lyndon word
palindrome
unbordered word
uniform recurrence – linear recurrence
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Summary: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.
Bibliography:hamoon.mousavi@gmail.com; shallit@uwaterloo.ca
istex:1FE785C2288FDC7D3BAF22770E2F06412D64A505
PII:S0988375416000102
publisher-ID:ita160024
ark:/67375/80W-D018PJWH-R
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0988-3754
1290-385X
DOI:10.1051/ita/2016010