Context-Free Languages and Primitive Words

A word is said to be primitive if it cannot be represented as any power of another word. It is a well-known conjecture that the set of all primitive words Q over a non-trivial alphabet is not context-free: this conjecture is still open. In this book, the authors deal with properties of primitive words over a non-primitive alphabet, the language consisting of all primitive words and related languages. Moreover, some decidable and undecidable problems with respect to the above languages are discussed as well. As another try, a search for a non-phrase structure grammar which generates Q is performed.

Contents:

• Preliminaries
• Combinatorial Properties of Words and Languages
• Rewriting Systems
• Iteration Lemmata
• Other Characterizations of Context-Free Languages
• Bounded and Palindromic Languages
• Further Combinatorial Investigations on Primitive Words
• Some Properties of the Language of Primitive Words
• Primitive Words in Languages
• Kászonyi-Katsura Theory
• Derivating Primitive Words
• Decidability, Roots, Multisets
• Context-Free Languages and Non-primitive Words
• Primitive Words and Palindromes
• Marcus Contextual Grammars and Primitive Words
• Appendices

Readership: Researchers, lecturers, senior undergraduates and graduate students in theoretical computer science.