Overview

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: PreliminariesCombinatorial Properties of Words and LanguagesRewriting SystemsIteration LemmataOther Characterizations of Context-Free LanguagesBounded and Palindromic LanguagesFurther Combinatorial Investigations on Primitive WordsSome Properties of the Language of Primitive WordsPrimitive Words in LanguagesKászonyi-Katsura TheoryDerivating Primitive WordsDecidability, Roots, MultisetsContext-Free Languages and Non-primitive WordsPrimitive Words and PalindromesMarcus Contextual Grammars and Primitive WordsAppendicesReadership: Researchers, lecturers, senior undergraduates and graduate students in theoretical computer science.

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9781322293769

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