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Formal Languages, Automata and Numeration Systems

Rigo, Michel

9781848216150 - Formal Languages, Automata and Numeration Systems

Artikelomschrijving

Formal Languages, Automaton and Numeration Systems presents readers with a review of research related to formal language theory, combinatorics on words or numeration systems, such as Words, DLT (Developments in Language Theory), ICALP, MFCS (Mathematical Foundation of Computer Science), Mons Theoretical Computer Science Days, Numeration, CANT (Combinatorics, Automata and Number Theory). Combinatorics on words deals with problems that can be stated in a non-commutative monoid, such as subword complexity of finite or infinite words, construction and properties of infinite words, unavoidable regularities or patterns. When considering some numeration systems, any integer can be represented as a finite word over an alphabet of digits. This simple observation leads to the study of the relationship between the arithmetical properties of the integers and the syntactical properties of the corresponding representations. One of the most profound results in this direction is given by the celebrated theorem by Cobham. Surprisingly, a recent extension of this result to complex numbers led to the famous Four Exponentials Conjecture. This is just one example of the fruitful relationship between formal language theory (including the theory of automata) and number theory. Contents to include: - algebraic structures, homomorphisms, relations, free monoid - finite words, prefixes, suffixes, factors, palindromes - periodicity and Fine-Wilf theorem - infinite words are sequences over a finite alphabet - properties of an ultrametric distance, example of the p-adic norm - topology of the set of infinite words - converging sequences of infinite and finite words, compactness argument - iterated morphism, coding, substitutive or morphic words - the typical example of the Thue-Morse word - the Fibonacci word, the Mex operator, the n-bonacci words - wordscomingfromnumbertheory(baseexpansions, continuedfractions, ...) - the taxonomy of Lindenmayer systems - S-adic sequences, Kolakoski word - re

Specificaties

Auteur Rigo, Michel
ISBN/EAN 9781848216150
Druk 1
€ 143,77 € 159,74
Verwachte bezorgdatum: 10-04

Artikelomschrijving

Formal Languages, Automaton and Numeration Systems presents readers with a review of research related to formal language theory, combinatorics on words or numeration systems, such as Words, DLT (Developments in Language Theory), ICALP, MFCS (Mathematical Foundation of Computer Science), Mons Theoretical Computer Science Days, Numeration, CANT (Combinatorics, Automata and Number Theory). Combinatorics on words deals with problems that can be stated in a non-commutative monoid, such as subword complexity of finite or infinite words, construction and properties of infinite words, unavoidable regularities or patterns. When considering some numeration systems, any integer can be represented as a finite word over an alphabet of digits. This simple observation leads to the study of the relationship between the arithmetical properties of the integers and the syntactical properties of the corresponding representations. One of the most profound results in this direction is given by the celebrated theorem by Cobham. Surprisingly, a recent extension of this result to complex numbers led to the famous Four Exponentials Conjecture. This is just one example of the fruitful relationship between formal language theory (including the theory of automata) and number theory. Contents to include: - algebraic structures, homomorphisms, relations, free monoid - finite words, prefixes, suffixes, factors, palindromes - periodicity and Fine-Wilf theorem - infinite words are sequences over a finite alphabet - properties of an ultrametric distance, example of the p-adic norm - topology of the set of infinite words - converging sequences of infinite and finite words, compactness argument - iterated morphism, coding, substitutive or morphic words - the typical example of the Thue-Morse word - the Fibonacci word, the Mex operator, the n-bonacci words - wordscomingfromnumbertheory(baseexpansions, continuedfractions, ...) - the taxonomy of Lindenmayer systems - S-adic sequences, Kolakoski word - re

Specificaties

Auteur Rigo, Michel
ISBN/EAN 9781848216150
Druk 1