The research results published in this volume range from pure mathematical theory (semigroup theory, discrete mathematics, and so on) to theoretical computer science, in particular formal languages and automata. The papers are the proceedings of the Third International Colloquium on Words, Languages and Combinatorics, and they address issues in the algebraic and combinatorial theories of semigroups, words and languages, the structure theory of automata, the classification theory of formal languages and codes, and applications of these theories to various areas, like quantum and molecular computing, coding theory, and cryptography.

The research results published in this book range from pure mathematical theory (semigroup theory, discrete mathematics, etc.) to theoretical computer science, in particular formal languages and automata. The papers address issues in the algebraic and combinatorial theories of semigroups, words and languages, the structure theory of automata, the classification theory of formal languages and codes, and applications of these theories to various areas, like quantum and molecular computing, coding theory, and cryptography.

The research results published in this set of proceedings range from pure semigroup theory to theoretical computer science, in particular formal languages and automata. Contributed by internationally recognized researchers, the papers address issues in the algebraic and combinatorial theories of semigroups, the structure theory of automata, the classification theory of formal languages and codes and applications of these theories to various areas like circuit testing, coding theory, or cryptography. The underlying theme is the semigroup and automaton theories and their role in certain applications.

Combinatorics on words, or finite sequences, is a field which grew simultaneously within disparate branches of mathematics such as group theory and probability. It has grown into an independent theory finding substantial applications in computer science automata theory and liguistics. This volume is the first to present a thorough treatment of this theory. All of the main results and techniques are covered. The presentation is accessible to undergraduate and graduate level students in mathematics and computer science as well as to specialists in all branches of applied mathematics.

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.

This book constitutes the refereed proceedings of the 9th International Conference on Combinatorics on Words, WORDS 2013, held in Turku, Finland, in September 2013 under the auspices of the EATCS. The 20 revised full papers presented were carefully reviewed and selected from 43 initial submissions. The central topic of the conference is combinatorics on words (i.e. the study of finite and infinite sequence of symbols) from varying points of view, including their combinatorial, algebraic and algorithmic aspects, as well as their applications.