The Undecidability of the Domino Problem

The Undecidability of the Domino Problem

PDF The Undecidability of the Domino Problem Download

  • Author: Robert Berger
  • Publisher: American Mathematical Soc.
  • ISBN: 0821812661
  • Category : Counting
  • Languages : en
  • Pages : 72


Logic and Theory of Algorithms

Logic and Theory of Algorithms

PDF Logic and Theory of Algorithms Download

  • Author: Arnold Beckmann
  • Publisher: Springer
  • ISBN: 3540694072
  • Category : Computers
  • Languages : en
  • Pages : 596

CiE 2008: Logic and Theory of Algorithms Athens, Greece, June 15–20, 2008 Computability in Europe (CiE) is an informal network of European scientists working on computability theory, including its foundations, technical devel- ment, and applications. Among the aims of the network is to advance our t- oretical understanding of what can and cannot be computed, by any means of computation. Its scienti?c vision is broad: computations may be performed with discrete or continuous data by all kinds of algorithms, programs, and - chines. Computations may be made by experimenting with any sort of physical system obeying the laws of a physical theory such as Newtonian mechanics, quantum theory, or relativity. Computations may be very general, depending on the foundations of set theory; or very speci?c, using the combinatorics of ?nite structures. CiE also works on subjects intimately related to computation, especially theories of data and information, and methods for formal reasoning about computations. The sources of new ideas and methods include practical developments in areas such as neural networks, quantum computation, natural computation, molecular computation, computational learning. Applications are everywhere,especially, in algebra,analysisand geometry, or data types and p- gramming. Within CiE there is general recognition of the underlying relevance of computability to physics and a broad range of other sciences, providing as it does a basic analysis of the causal structure of dynamical systems. Thisvolume,Logic andTheory of Algorithms,istheproceedingsofthefourth in a series of conferences of CiE that was held at the University of Athens, June 15–20, 2008.


The Classical Decision Problem

The Classical Decision Problem

PDF The Classical Decision Problem Download

  • Author: Egon Börger
  • Publisher: Springer Science & Business Media
  • ISBN: 9783540423249
  • Category : Mathematics
  • Languages : en
  • Pages : 500

This book offers a comprehensive treatment of the classical decision problem of mathematical logic and of the role of the classical decision problem in modern computer science. The text presents a revealing analysis of the natural order of decidable and undecidable cases and includes a number of simple proofs and exercises.


Substitution and Tiling Dynamics: Introduction to Self-inducing Structures

Substitution and Tiling Dynamics: Introduction to Self-inducing Structures

PDF Substitution and Tiling Dynamics: Introduction to Self-inducing Structures Download

  • Author: Shigeki Akiyama
  • Publisher: Springer Nature
  • ISBN: 3030576663
  • Category : Mathematics
  • Languages : en
  • Pages : 456

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.


Sequences, Groups, and Number Theory

Sequences, Groups, and Number Theory

PDF Sequences, Groups, and Number Theory Download

  • Author: Valérie Berthé
  • Publisher: Birkhäuser
  • ISBN: 331969152X
  • Category : Mathematics
  • Languages : en
  • Pages : 578

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.


Reachability Problems

Reachability Problems

PDF Reachability Problems Download

  • Author: Igor Potapov
  • Publisher: Springer Science & Business Media
  • ISBN: 3642044190
  • Category : Computers
  • Languages : en
  • Pages : 243

This book constitutes the research papers presented at the 3rd International Workshop, RP 2009 held in Palaiseau, France, September 23-25, 2009. The 20 full papers of this workshop reflect reachability problems that appear in algebraic structures, computational models, hybrid systems and verification. Reachability is a fundamental problem in the context of many models and abstractions which are describing various computational processes. Topics of interest include reachability problems in infinite state systems, rewriting systems, dynamical and hybrid systems, reachability problems in logic and verification, reachability analysis in different computational models, counter, timed, cellular, communicating automata, Petri-Nets, computational aspects of algebraic structures and predictability in iterative maps and new computational paradigms.


Reachability Problems

Reachability Problems

PDF Reachability Problems Download

  • Author: Olivier Bournez
  • Publisher: Springer
  • ISBN: 3642044204
  • Category : Computers
  • Languages : en
  • Pages : 233

This book constitutes the research papers presented at the 3rd International Workshop, RP 2009 held in Palaiseau, France, September 23-25, 2009. The 20 full papers of this workshop reflect reachability problems that appear in algebraic structures, computational models, hybrid systems and verification. Reachability is a fundamental problem in the context of many models and abstractions which are describing various computational processes. Topics of interest include reachability problems in infinite state systems, rewriting systems, dynamical and hybrid systems, reachability problems in logic and verification, reachability analysis in different computational models, counter, timed, cellular, communicating automata, Petri-Nets, computational aspects of algebraic structures and predictability in iterative maps and new computational paradigms.


Cellular Automata and Discrete Complex Systems

Cellular Automata and Discrete Complex Systems

PDF Cellular Automata and Discrete Complex Systems Download

  • Author: Jarkko Kari
  • Publisher: Springer
  • ISBN: 366247221X
  • Category : Computers
  • Languages : en
  • Pages : 263

This volume constitutes the thoroughly refereed proceedings of the 21st International Workshop on Cellular Automata and Discrete Complex Systems, AUTOMATA 2015, held in Turku, Finland, in June 2015. This volume contains 4 invited talks in full-paper length and 15 regular papers, which were carefully reviewed and selected from a total of 33 submissions. Topics of interest include, the following aspects and features of such systems: dynamical, topological, ergodic and algebraic aspects; algorithmic and complexity issues; emergent properties; formal language processing aspects; symbolic dynamics; models of parallelism and distributed systems; timing schemes; phenomenological descriptions; scientific modeling; and practical applications.


Algorithmics

Algorithmics

PDF Algorithmics Download

  • Author: David Harel
  • Publisher: Pearson Education
  • ISBN: 9780321117847
  • Category : Computers
  • Languages : en
  • Pages : 540

The best selling 'Algorithmics' presents the most important, concepts, methods and results that are fundamental to the science of computing. It starts by introducing the basic ideas of algorithms, including their structures and methods of data manipulation. It then goes on to demonstrate how to design accurate and efficient algorithms, and discusses their inherent limitations. As the author himself says in the preface to the book; 'This book attempts to present a readable account of some of the most important and basic topics of computer science, stressing the fundamental and robust nature of the science in a form that is virtually independent of the details of specific computers, languages and formalisms'.


Reachability Problems

Reachability Problems

PDF Reachability Problems Download

  • Author: Sylvain Schmitz
  • Publisher: Springer Nature
  • ISBN: 3030617394
  • Category : Computers
  • Languages : en
  • Pages : 165

This book constitutes the refereed proceedings of the 14th International Conference on Reachability Problems, RP 2020, held in Paris, France in October 2020. The 8 full papers presented were carefully reviewed and selected from 25 submissions. In addition, 2 invited papers were included in this volume. The papers cover topics such as reachability for infinite state systems; rewriting systems; reachability analysis in counter/timed/cellular/communicating automata; Petri nets; computational aspects of semigroups, groups, and rings; reachability in dynamical and hybrid systems; frontiers between decidable and undecidable reachability problems; complexity and decidability aspects; predictability in iterative maps; and new computational paradigms.