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: ac algebraic structures, homomorphisms, relations, free monoid ac finite words, prefixes, suffixes, factors, palindromes ac periodicity and FineaWilf theorem ac infinite words are sequences over a finite alphabet ac properties of an ultrametric distance, example of the p-adic norm ac topology of the set of infinite words ac converging sequences of infinite and finite words, compactness argument ac iterated morphism, coding, substitutive or morphic words ac the typical example of the ThueaMorse word ac the Fibonacci word, the Mex operator, the n-bonacci words ac wordscomingfromnumbertheory(baseexpansions, continuedfractions, ...) ac the taxonomy of Lindenmayer systems ac S-adic sequences, Kolakoski word ac repetition in words, avoiding repetition, repetition threshold ac (complete) de Bruijn graphs ac concepts from computability theory and decidability issues ac Post correspondence problem and application to mortality of matrices ac origins of combinatorics on words ac bibliographic notes ac languages of finite words, regular languages ac factorial, prefix/suffix closed languages, trees and codes ac unambiguous and deterministic automata, Kleeneas theorem ac growth function of regular languages ac non-deterministic automata and determinization ac radix order, first word of each length and decimation of a regular language ac the theory of the minimal automata ac an introduction to algebraic automata theory, the syntactic monoid and the syntactic complexity ac star-free languages and a theorem of Schu Itzenberger ac rational formal series and weighted automata ac context-free languages, pushdown automata and grammars ac growth function of context-free languages, Parikhas theorem ac some decidable and undecidable problems in formal language theory ac bibliographic notes ac factor complexity, MorseaHedlund theorem ac arithmetic complexity, Van Der Waerden theorem, pattern complexity ac recurrence, uniform recurrence, return words ac Sturmian words, coding of rotations, Kroneckeras theorem ac frequencies of letters, factors and primitive morphism ac critical exponent ac factor complexity of automatic se[HOL 98] HOLLANDER M., aGreedy numeration systems and regularitya, Theory of Computer Systems, vol. ... [HOP 79] HOPCROFT J.E., ULLMAN J.D., Introduction to Automata Theory, Languages, and Computation, AddisonWesley, 1979.

Title | : | Formal Languages, Automata and Numeration Systems |

Author | : | Michel Rigo |

Publisher | : | John Wiley & Sons - 2014-09-10 |

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