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Author: Michel Rigo
Publisher: Wiley-ISTE
ISBN: 9781848216150
Category : Computers
Languages : en
Pages : 0
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Book Description
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.
Author: Michel Rigo
Publisher: Wiley-ISTE
ISBN: 9781848216150
Category : Computers
Languages : en
Pages : 0
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Book Description
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.
Author: Michel Rigo
Publisher: John Wiley & Sons
ISBN: 1119008220
Category : Computers
Languages : en
Pages : 330
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Book Description
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.
Author: Michel Rigo
Publisher: John Wiley & Sons
ISBN: 1119042860
Category : Technology & Engineering
Languages : en
Pages : 151
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Book Description
The interplay between words, computability, algebra and arithmetic has now proved its relevance and fruitfulness. Indeed, the cross-fertilization between formal logic and finite automata (such as that initiated by J.R. Büchi) or between combinatorics on words and number theory has paved the way to recent dramatic developments, for example, the transcendence results for the real numbers having a "simple" binary expansion, by B. Adamczewski and Y. Bugeaud. This book is at the heart of this interplay through a unified exposition. Objects are considered with a perspective that comes both from theoretical computer science and mathematics. Theoretical computer science offers here topics such as decision problems and recognizability issues, whereas mathematics offers concepts such as discrete dynamical systems. The main goal is to give a quick access, for students and researchers in mathematics or computer science, to actual research topics at the intersection between automata and formal language theory, number theory and combinatorics on words. The second of two volumes on this subject, this book covers regular languages, numeration systems, formal methods applied to decidability issues about infinite words and sets of numbers.
Author: Michel Rigo
Publisher:
ISBN: 9781119042853
Category : Combination (Linguistics)
Languages : en
Pages : 245
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Book Description
Author: Shigeki Akiyama
Publisher: Springer Nature
ISBN: 3030576663
Category : Mathematics
Languages : en
Pages : 456
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Book Description
This book presents a panorama of recent developments in the theory of tilings and related dynamical systems. It contains an expanded version of courses given in 2017 at the research school associated with the Jean-Morlet chair program. Tilings have been designed, used and studied for centuries in various contexts. This field grew significantly after the discovery of aperiodic self-similar tilings in the 60s, linked to the proof of the undecidability of the Domino problem, and was driven futher by Dan Shechtman's discovery of quasicrystals in 1984. Tiling problems establish a bridge between the mutually influential fields of geometry, dynamical systems, aperiodic order, computer science, number theory, algebra and logic. The main properties of tiling dynamical systems are covered, with expositions on recent results in self-similarity (and its generalizations, fusions rules and S-adic systems), algebraic developments connected to physics, games and undecidability questions, and the spectrum of substitution tilings.
Author: Peter Linz
Publisher: Jones & Bartlett Publishers
ISBN:
Category : Computers
Languages : en
Pages : 408
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Book Description
An Introduction to Formal Languages & Automata provides an excellent presentation of the material that is essential to an introductory theory of computation course. The text was designed to familiarize students with the foundations & principles of computer science & to strengthen the students' ability to carry out formal & rigorous mathematical argument. Employing a problem-solving approach, the text provides students insight into the course material by stressing intuitive motivation & illustration of ideas through straightforward explanations & solid mathematical proofs. By emphasizing learning through problem solving, students learn the material primarily through problem-type illustrative examples that show the motivation behind the concepts, as well as their connection to the theorems & definitions.
Author: Jeffrey Shallit
Publisher: Cambridge University Press
ISBN: 0521865727
Category : Computers
Languages : en
Pages : 0
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Book Description
A textbook for a graduate course on formal languages and automata theory, building on prior knowledge of theoretical computer models.
Author: Masami Ito
Publisher: World Scientific
ISBN: 9814317608
Category : Mathematics
Languages : en
Pages : 247
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Book Description
This volume consists of papers selected from the presentations at the workshop and includes mainly recent developments in the fields of formal languages, automata theory and algebraic systems related to the theoretical computer science and informatics. It covers the areas such as automata and grammars, languages and codes, combinatorics on words, cryptosystems, logics and trees, Grobner bases, minimal clones, zero-divisor graphs, fine convergence of functions, and others.
Author: Kamala Krithivasan
Publisher: Pearson Education India
ISBN: 9788131723562
Category : Computable functions
Languages : en
Pages : 446
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Book Description
Introduction to Formal Languages, Automata Theory and Computation presents the theoretical concepts in a concise and clear manner, with an in-depth coverage of formal grammar and basic automata types. The book also examines the underlying theory and principles of computation and is highly suitable to the undergraduate courses in computer science and information technology. An overview of the recent trends in the field and applications are introduced at the appropriate places to stimulate the interest of active learners.
Author: S.P.Eugene Xavier
Publisher: New Age International
ISBN: 8122416551
Category : Computational complexity
Languages : en
Pages : 35
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Book Description
This Book Is Aimed At Providing An Introduction To The Basic Models Of Computability To The Undergraduate Students. This Book Is Devoted To Finite Automata And Their Properties. Pushdown Automata Provides A Class Of Models And Enables The Analysis Of Context-Free Languages. Turing Machines Have Been Introduced And The Book Discusses Computability And Decidability. A Number Of Problems With Solutions Have Been Provided For Each Chapter. A Lot Of Exercises Have Been Given With Hints/Answers To Most Of These Tutorial Problems.
