Deciding Properties Of Automatic Sequences
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Deciding Properties Of Automatic Sequences
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Author : Luke Schaeffer
language : en
Publisher:
Release Date : 2013
Deciding Properties Of Automatic Sequences written by Luke Schaeffer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
In this thesis, we show that several natural questions about automatic sequences can be expressed as logical predicates and then decided mechanically. We extend known results in this area to broader classes of sequences (e.g., paperfolding words), introduce new operations that extend the space of possible queries, and show how to process the results.
Automatic Sequences
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Author : Jean-Paul Allouche
language : en
Publisher: Cambridge University Press
Release Date : 2003-07-21
Automatic Sequences written by Jean-Paul Allouche and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-21 with Computers categories.
Uniting dozens of seemingly disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences generated by 'finite automata'. The authors apply the theory to the study of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. And further, they provide applications to number theory (particularly to formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Starting from first principles wherever feasible, basic results from combinatorics on words, numeration systems, and models of computation are discussed. Thus this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this fascinating subject. Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and over 1600 citations to the literature.
Automatic Sequences
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Author : von Friedrich Haeseler
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22
Automatic Sequences written by von Friedrich Haeseler and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.
Automatic sequences are sequences which are produced by a finite automaton. Although they are not random they may look as being random. They are complicated, in the sense of not being not ultimately periodic, they may look rather complicated, in the sense that it may not be easy to name the rule by which the sequence is generated, however there exists a rule which generates the sequence. The concept automatic sequences has special applications in algebra, number theory, finite automata and formal languages, combinatorics on words. The text deals with different aspects of automatic sequences, in particular: · a general introduction to automatic sequences · the basic (combinatorial) properties of automatic sequences · the algebraic approach to automatic sequences · geometric objects related to automatic sequences.
Automatic Sequences And Decidable Properties
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Author : Daniel Goc
language : en
Publisher:
Release Date : 2013
Automatic Sequences And Decidable Properties written by Daniel Goc and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
In 1912 Axel Thue sparked the study of combinatorics on words when he showed that the Thue-Morse sequence contains no overlaps, that is, factors of the form ayaya. Since then many interesting properties of sequences began to be discovered and studied. In this thesis, we consider a class of infinite sequences generated by automata, called the k-automatic sequences. In particular, we present a logical theory in which many properties of k-automatic sequences can be expressed as predicates and we show that such predicates are decidable. Our main contribution is the implementation of a theorem prover capable of practically characterizing many commonly sought-after properties of k-automatic sequences. We showcase a panoply of results achieved using our method. We give new explicit descriptions of the recurrence and appearance functions of a list of well-known k-automatic sequences. We define a related function, called the condensation function, and give explicit descriptions for it as well. We re-affirm known results on the critical exponent of some sequences and determine it for others where it was previously unknown. On the more theoretical side, we show that the subword complexity p(n) of k-automatic sequences is k-synchronized, i.e., the language of pairs (n, p(n)) (expressed in base k) is accepted by an automaton. Furthermore, we prove that the Lyndon factorization of k-automatic sequences is also k-automatic and explicitly compute the factorization for several sequences. Finally, we show that while the number of unbordered factors of length n is not k-synchronized, it is k-regular.
The Logical Approach To Automatic Sequences
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Author : Jeffrey Shallit
language : en
Publisher: Cambridge University Press
Release Date : 2022-09-29
The Logical Approach To Automatic Sequences written by Jeffrey Shallit and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-29 with Computers categories.
Learn how to automatically prove mathematical statements in combinatorics, sequences, and number theory.
Sequences Groups And Number Theory
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Author : Valérie Berthé
language : en
Publisher: Birkhäuser
Release Date : 2018-04-09
Sequences Groups And Number Theory written by Valérie Berthé and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-09 with Mathematics categories.
This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.
Computer Science Theory And Applications
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Author : Andrei A. Bulatov
language : en
Publisher: Springer
Release Date : 2013-06-03
Computer Science Theory And Applications written by Andrei A. Bulatov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-03 with Computers categories.
This book constitutes the proceedings of the 8th International Computer Science Symposium in Russia, CSR 2013, held in Ekaterinburg, Russia, in June 2013. The 29 full papers presented in this volume were carefully reviewed and selected from 52 submissions. In addition the book contains 8 invited lectures. The papers are organized in topical sections on: algorithms; automata; logic and proof complexity; complexity; words and languages; and logic and automata.
Evolving Computability
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Author : Arnold Beckmann
language : en
Publisher: Springer
Release Date : 2015-06-19
Evolving Computability written by Arnold Beckmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-19 with Computers categories.
This book constitutes the refereed proceedings of the 11th Conference on Computability in Europe, CiE 2015, held in Bucharest, Romania, in June/July 2015. The 26 revised papers presented were carefully reviewed and selected from 64 submissions and included together with 10 invited papers in this proceedings. The conference CiE 2015 has six special sessions: two sessions, Representing Streams and Reverse Mathematics, were introduced for the first time in the conference series. In addition to this, new developments in areas frequently covered in the CiE conference series were addressed in the further special sessions on Automata, Logic and Infinite Games; Bio-inspired Computation; Classical Computability Theory; as well as History and Philosophy of Computing.
Combinatorics Words And Symbolic Dynamics
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Author : Valérie Berthé
language : en
Publisher: Cambridge University Press
Release Date : 2016-02-26
Combinatorics Words And Symbolic Dynamics written by Valérie Berthé and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-26 with Computers categories.
Surveys trends arising from the applications and interactions between combinatorics, symbolic dynamics and theoretical computer science.
Automated Reasoning
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Author : Christoph Benzmüller
language : en
Publisher: Springer Nature
Release Date :
Automated Reasoning written by Christoph Benzmüller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.