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Author: Martin Grohe
Publisher: Cambridge University Press
ISBN: 1108234305
Category : Mathematics
Languages : en
Pages : 554
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Book Description
Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book approaches descriptive complexity from the angle of modern structural graph theory, specifically graph minor theory. It develops a 'definable structure theory' concerned with the logical definability of graph theoretic concepts such as tree decompositions and embeddings. The first part starts with an introduction to the background, from logic, complexity, and graph theory, and develops the theory up to first applications in descriptive complexity theory and graph isomorphism testing. It may serve as the basis for a graduate-level course. The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decidable in polynomial time if, and only if, they are definable in fixed-point logic with counting.
Author: Martin Grohe
Publisher: Cambridge University Press
ISBN: 1108234305
Category : Mathematics
Languages : en
Pages : 554
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Book Description
Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book approaches descriptive complexity from the angle of modern structural graph theory, specifically graph minor theory. It develops a 'definable structure theory' concerned with the logical definability of graph theoretic concepts such as tree decompositions and embeddings. The first part starts with an introduction to the background, from logic, complexity, and graph theory, and develops the theory up to first applications in descriptive complexity theory and graph isomorphism testing. It may serve as the basis for a graduate-level course. The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decidable in polynomial time if, and only if, they are definable in fixed-point logic with counting.
Author: Alessandra Palmigiano
Publisher: Springer Nature
ISBN: 3031241177
Category : Philosophy
Languages : en
Pages : 1149
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Book Description
Samson Abramsky’s wide-ranging contributions to logical and structural aspects of Computer Science have had a major influence on the field. This book is a rich collection of papers, inspired by and extending Abramsky’s work. It contains both survey material and new results, organised around six major themes: domains and duality, game semantics, contextuality and quantum computation, comonads and descriptive complexity, categorical and logical semantics, and probabilistic computation. These relate to different stages and aspects of Abramsky’s work, reflecting its exceptionally broad scope and his ability to illuminate and unify diverse topics. Chapters in the volume include a review of his entire body of work, spanning from philosophical aspects to logic, programming language theory, quantum theory, economics and psychology, and relating it to a theory of unification of sciences using dual adjunctions. The section on game semantics shows how Abramsky’s work has led to a powerful new paradigm for the semantics of computation. The work on contextuality and categorical quantum mechanics has been highly influential, and provides the foundation for increasingly widely used methods in quantum computing. The work on comonads and descriptive complexity is building bridges between currently disjoint research areas in computer science, relating Structure to Power. The volume also includes a scientific autobiography, and an overview of the contributions. The outstanding set of contributors to this volume, including both senior and early career academics, serve as testament to Samson Abramsky’s enduring influence. It will provide an invaluable and unique resource for both students and established researchers.
Author: Rosalie Iemhoff
Publisher: Springer
ISBN: 3662595338
Category : Mathematics
Languages : en
Pages : 683
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Book Description
Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 26th Workshop on Logic, Language, Information and Communication, WoLLIC 2019, held in Utrecht, The Netherlands, in July 2019. The 41 full papers together with 6 invited lectures presented were fully reviewed and selected from 60 submissions. The idea is to have a forum which is large enough in the number of possible interactions between logic and the sciences related to information and computation, and yet is small enough to allow for concrete and useful interaction among participants.
Author: Konrad K. Dabrowski
Publisher: Cambridge University Press
ISBN: 1009018884
Category : Mathematics
Languages : en
Pages : 379
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Book Description
These nine articles provide up-to-date surveys of topics of contemporary interest in combinatorics.
Author: Cyrus F. Nourani
Publisher: CRC Press
ISBN: 1771882484
Category : Mathematics
Languages : en
Pages : 304
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Book Description
This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples
Author: Byunghan Kim
Publisher: World Scientific
ISBN: 9813237562
Category : Mathematics
Languages : en
Pages : 310
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Book Description
The Asian Logic Conference (ALC) is a major international event in mathematical logic. It features the latest scientific developments in the fields of mathematical logic and its applications, logic in computer science, and philosophical logic. The ALC series also aims to promote mathematical logic in the Asia-Pacific region and to bring logicians together both from within Asia and elsewhere for an exchange of information and ideas. This combined proceedings volume represents works presented or arising from the 14th and 15th ALCs.
Author: Isolde Adler
Publisher: Springer Nature
ISBN: 3030604403
Category : Computers
Languages : en
Pages : 430
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Book Description
This book constitutes the revised papers of the 46th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2020, held in Leeds, UK, in June 2020. The workshop was held virtually due to the COVID-19 pandemic. The 32 full papers presented in this volume were carefully reviewed and selected from 94 submissions. They cover a wide range of areas, aiming to present emerging research results and to identify and explore directions of future research of concepts on graph theory and how they can be applied to various areas in computer science.
Author: Rodney G. Downey
Publisher: Springer Science & Business Media
ISBN: 1447155599
Category : Computers
Languages : en
Pages : 765
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Book Description
This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research. Features: describes many of the standard algorithmic techniques available for establishing parametric tractability; reviews the classical hardness classes; explores the various limitations and relaxations of the methods; showcases the powerful new lower bound techniques; examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach; demonstrates how complexity methods and ideas have evolved over the past 25 years.
Author: Luis Felipe Tabera Alonso
Publisher: Ed. Universidad de Cantabria
ISBN: 8419024023
Category : Mathematics
Languages : en
Pages : 335
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Book Description
El congreso Discrete Mathematics Days (DMD20/22) tendrá lugar del 4 al 6 de julio de 2022, en la Facultad de Ciencias de la Universidad de Cantabria (Santander, España). Este congreso internacional se centra en avances dentro del campo de la Matemática discreta, incluyendo, de manera no exhaustiva: · Algoritmos y Complejidad · Combinatoria · Teoría de Códigos · Criptografía · Geometría Discreta y Computacional · Optimización Discreta · Teoría de Grafos · Problemas de localización discreta y temas relacionados Las ediciones anteriores de este evento se celebraros en Sevilla (2018) y Barcelona (2016), estos congresos heredan la tradición de las Jornadas de Matemática Discreta y Algorítmica (JMDA), el encuentro bienal en España en Matemática Discreta (desde 1998). Durante la celebración del congreso tendrán lugar cuatro conferencias plenarias, cuarenta y dos presentaciones orales y una sesión de once pósteres. Abstract The Discrete Mathematics Days (DMD20/22) will be held on July 4-6, 2022, at Facultad de Ciencias of the Universidad de Cantabria (Santander, Spain). The main focus of this international conference is on current topics in Discrete Mathematics, including (but not limited to): Algorithms and Complexity Combinatorics Coding Theory Cryptography Discrete and Computational Geometry Discrete Optimization Graph Theory Location and Related Problems The previous editions were held in Sevilla in 2018 and in Barcelona in 2016, inheriting the tradition of the Jornadas de Matemática Discreta y Algorítmica (JMDA), the Spanish biennial meeting (since 1998) on Discrete Mathematics. The program consists on four plenary talks, 42 contributed talks and a poster session with 11 contributions.
Author: Alexander A. Ivanov
Publisher: Cambridge University Press
ISBN: 1009338048
Category : Mathematics
Languages : en
Pages : 583
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Book Description
The current state of knowledge on the Monster group, including Majorana theory, Vertex Operator Algebras, Moonshine and maximal subgroups.
