Journal of the ACM (JACM)
Finding Maximal Repetitions in a Word in Linear Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Handbook of Exact String Matching Algorithms
Handbook of Exact String Matching Algorithms
The number of runs in a string: improved analysis of the linear upper bound
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Sturmian graphs and a conjecture of moser
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
The number of runs in a string
Information and Computation
The Number of Runs in Sturmian Words
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
Repetitions in strings: Algorithms and combinatorics
Theoretical Computer Science
Sturmian and episturmian words: a survey of some recent results
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
A simple representation of subwords of the Fibonacci word
Information Processing Letters
Sturmian graphs and integer representations over numeration systems
Discrete Applied Mathematics
On the structure of compacted subword graphs of Thue-Morse words and their applications
Journal of Discrete Algorithms
On the maximal number of cubic runs in a string
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
The maximal number of cubic runs in a word
Journal of Computer and System Sciences
Computing the number of cubic runs in standard Sturmian words
Discrete Applied Mathematics
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We use automata-theoretic approach to analyze properties of Fibonacci words. The directed acyclic subword graph (dawg) is a useful deterministic automaton accepting all suffixes of the word. We show that dawg's of Fibonacci words have particularly simple structure. Our main result is a unifying framework for a large collection of relatively simple properties of Fibonacci words. The simple structure of dawgs of Fibonacci words gives in many cases simplified alternative proofs and new interpretation of several well-known properties of Fibonacci words. In particular, the structure of lengths of paths corresponds to a number-theoretic characterization of occurrences of any subword. Using the structural properties of dawg's it can be easily shown that for a string ω we can check if ω is a subword of a Fibonacci word in time O(|ω|) and O(1) space. Compact dawg's of Fibonacci words show a very regular structure of their suffix trees and show how the suffix tree for the Fibonacci word grows (extending the leaves in a very simple way) into the suffix tree for the next Fibonacci word.