Usefulness of Directed Acyclic Subword Graphs in Problems Related to Standard Sturmian Words

The class of finite Sturmian words consists of words having particularly simple compressed representation, which is a generalization of the Fibonacci recurrence for Fibonacci words. The subword graphs of these words (especially their compacted versions) have a very special regular structure. In this paper we investigate this structure in more detail than in the previous papers and show how several syntactical properties of Sturmian words follow from their graph properties. Consequently simple alternative graph-based proofs of several known facts are presented. The very special structure of subword graphs leads also to special easy algorithms computing some parameters of Sturmain words: the number of subwords, the critical factorization point, lexicographically maximal suffixes, occurrences of subwords of a fixed length, and right special factors. These algorithms work in linear time with respect to n, the size of the compressed representation of the standard word, though the words the...

• Type: Conference
• Year: 2008
• Where: STRINGOLOGY
• Authors: Pawel Baturo, Marcin Piatkowski, Wojciech Rytter
• Keywords: Fibonacci Words, Finite Sturmian Words, Programming Languages, STRINGOLOGY 2008, Sturmian Words