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The origins of combinatorics on words
, 2007
"... We investigate the historical roots of the field of combinatorics on words. They comprise applications and interpretations in algebra, geometry and combinatorial enumeration. These considerations gave rise to early results such as those of Axel Thue at the beginning of the 20th century. Other early ..."
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We investigate the historical roots of the field of combinatorics on words. They comprise applications and interpretations in algebra, geometry and combinatorial enumeration. These considerations gave rise to early results such as those of Axel Thue at the beginning of the 20th century. Other early results were obtained as a byproduct of investigations on various combinatorial objects. For example, paths in graphs are encoded by words in a natural way, and conversely, the Cayley graph of a group or a semigroup encodes words by paths. We give in this text an account of this twosided interaction.
Automata and Formal Languages
, 2003
"... This article provides an introduction to the theory of automata and formal languages. The elements are presented in a historical perspective and the links with other areas are underlined. In particular, applications of the field to linguistics, software design, text processing, computational alg ..."
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This article provides an introduction to the theory of automata and formal languages. The elements are presented in a historical perspective and the links with other areas are underlined. In particular, applications of the field to linguistics, software design, text processing, computational algebra or computational biology are given.
Mathematical Foundations of Automata Theory JeanÉric Pin
"... These notes form the core of a future book on the algebraic foundations of automata theory. This book is still incomplete, but the first eleven chapters now form a relatively coherent material, covering roughly the topics described below. The early years of automata theory Kleene’s theorem [43] is u ..."
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These notes form the core of a future book on the algebraic foundations of automata theory. This book is still incomplete, but the first eleven chapters now form a relatively coherent material, covering roughly the topics described below. The early years of automata theory Kleene’s theorem [43] is usually considered as the starting point of automata theory. It shows that the class of recognisable languages (that is, recognised by finite automata), coincides with the class of rational languages, which are given by rational expressions. Rational expressions can be thought of as a generalisationofpolynomials involvingthree operations: union (which playsthe role of addition), product and the star operation. It was quickly observed that these essentially combinatorial definitions can be interpreted in a very rich way in algebraic and logical terms. Automata over infinite words were introduced by Büchi in the early 1960s to solve decidability questions in the firstorder and monadic secondorder logic of one successor. Investigating the twosuccessor
Mathematical Foundations of Automata Theory JeanÉric Pin
, 2014
"... These notes form the core of a future book on the algebraic foundations of automata theory. This book is still incomplete, but the first eleven chapters now form a relatively coherent material, covering roughly the topics described below. The early years of automata theory Kleene’s theorem [49] is u ..."
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These notes form the core of a future book on the algebraic foundations of automata theory. This book is still incomplete, but the first eleven chapters now form a relatively coherent material, covering roughly the topics described below. The early years of automata theory Kleene’s theorem [49] is usually considered as the starting point of automata theory. It shows that the class of recognisable languages (that is, recognised by finite automata), coincides with the class of rational languages, which are given by rational expressions. Rational expressions can be thought of as a generalisation of polynomials involving three operations: union (which plays the role of addition), product and the star operation. It was quickly observed that these essentially combinatorial definitions can be interpreted in a very rich way in algebraic and logical terms. Automata over infinite words were introduced by Büchi in the early 1960s to solve decidability questions in firstorder and monadic secondorder logic of one successor. Investigating twosuccessor logic,