Primitive words and roots of words

In the algebraic theory of codes and formal languages, the set Q of all primitive words over some alphabet Σ has received special interest. With this survey article we give an overview about relevant research to this topic during the last twenty years including own investigations and some new results. In Section 1 after recalling the most important notions from formal language theory we illustrate the connection between coding theory and primitive words by some facts. We define primitive words as words having only a trivial representation as the power of another word. Nonprimitive words (without the empty word) are exactly the periodic words. Every nonempty word is a power of an uniquely determined primitive word which is called the root of the former one. The set of all roots of nonempty words of a language is called the root of the language. The primitive words have interesting combinatorial properties which we consider in Section 2. In Section 3 we investigate the relationship bet...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Gerhard Lischke
• Keywords: Chomsky Hierarchy, CORR 2011, Education, Formal Language, Primitive Words