The structure of subword graphs and suffix trees of fibonacci words

Document Type

Conference Proceeding

Publication Date

6-23-2006

Abstract

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. The simple structure of paths in these graphs gives simplified alternative proofs and new interpretation of several known properties of Fibonacci words. The structure of lengths of paths in the compacted subword graph corresponds to a number-theoretic characterization of occurrences of subwords in terms of Zeckendorff Fibonacci number system. Using the structural properties of dawg's it can be easily shown that for a string w we can check if w is a subword of a Fibonacci word in time O(|w|) 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. © Springer-Verlag Berlin Heidelberg 2006.

Identifier

33745160683 (Scopus)

ISBN

[3540310231, 9783540310235]

Publication Title

Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics

External Full Text Location

https://doi.org/10.1007/11605157_21

e-ISSN

16113349

ISSN

03029743

First Page

250

Last Page

261

Volume

3845 LNCS

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