Some combinatorial properties of the Thue-Morse sequence and a problem in semigroups
Theoretical Computer Science
On bispecial factors of the Thue-Morse word
Information Processing Letters
Text algorithms
Subword complexity of a generalized Thue-Morse word
Information Processing Letters
Reducing space for index implementation
Theoretical Computer Science
Direct Construction of Compact Directed Acyclic Word Graphs
CPM '97 Proceedings of the 8th Annual Symposium on Combinatorial Pattern Matching
The structure of subword graphs and suffix trees of Fibonacci words
Theoretical Computer Science - Implementation and application of automata
Discrete Applied Mathematics
On-line construction of compact directed acyclic word graphs
Discrete Applied Mathematics
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We investigate how syntactic properties of Thue-Morse words are related to special type of automata/graphs. The directed acyclic subword graph (dawg, in short) is a useful deterministic automaton accepting all suffixes of the word. Its compacted version (resulted by compressing chains of states) is denoted by cdawg. The cdawgs of Thue-Morse words have regular and very simple structure, in particular they offer a powerful (exponential) compression of the set of all subwords in case of finite Thue-Morse words. Using the special structure of cdawgs we present several unknown properties of Thue-Morse words as well as new (graph-based) proofs of some well-known properties. In particular we show a simple algorithm that checks, for a given string w, if w is a subword of a Thue-Morse word and computes its number of occurrences in n-th Thue-Morse word in O(|w|+logn) time and O(1) space. Additionally, a slight modification of the compact dawg of the infinite Thue-Morse word yields an infinite graph with 2-counting property.