The Power Of Computable Processes Unveiling The Foundations Of Logic And Mathematics
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The Power Of Computable Processes Unveiling The Foundations Of Logic And Mathematics
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-03-17
The Power Of Computable Processes Unveiling The Foundations Of Logic And Mathematics written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-17 with Science categories.
Embark on an enlightening journey into the captivating world of computability, where logic, mathematics, and the very nature of intelligence intertwine. This comprehensive book delves into the profound foundations of computability theory, unveiling its rich history, exploring its intricate connections to various disciplines, and showcasing its far-reaching implications for modern computing. Uncover the Roots of Computability: Discover the fascinating evolution of computability theory, from its early origins to the groundbreaking work of Alan Turing and beyond. Explore the concept of the Turing machine, a universal model of computation that revolutionized our understanding of computation. Investigate Church's Thesis, a fundamental hypothesis that asserts the equivalence of computability and effective calculability, and delve into the Entscheidungsproblem and Gödel's Incompleteness Theorems, which illuminate the limits of computability. Explore the Foundations of Logic: Delve into the intricate world of logic, the cornerstone of computability theory. Discover the power of propositional and predicate logic, uncovering the principles of logical reasoning and the intricacies of formal systems. Investigate completeness and soundness in first-order logic, exploring the relationship between provability and truth. Moreover, explore the applications of first-order logic in computer science, highlighting its role in automated reasoning and knowledge representation. Unravel Computable Functions and Their Properties: Embark on a journey into the realm of computable functions, the building blocks of computation. Investigate the definition of computable functions, examining primitive recursive functions and their closure properties. Encounter the concept of recursively enumerable functions and explore the infamous Halting Problem, a pivotal undecidable problem that has profound implications for the limits of computation. Additionally, examine Rice's Theorem, which sheds light on the inherent undecidability of many problems in computer science. Investigate Computability and Complexity: Dive into the captivating interplay between computability and complexity, two fundamental aspects of computation. Explore the concept of complexity classes, providing a framework for measuring the difficulty of computational problems. Delve into the cornerstones of complexity theory, namely P, NP, and NP-Completeness, and investigate the inherent challenges associated with intractable problems. Furthermore, examine polynomial-time algorithms, efficient solutions to tractable problems, and explore heuristics and approximation algorithms as strategies for dealing with intractable problems. Explore Computability and Automata Theory: Discover the deep connection between computability and automata theory, two powerful tools for understanding computation. Investigate finite automata, pushdown automata, and Turing machines, exploring their capabilities and limitations in recognizing different classes of formal languages. Delve into the Chomsky Hierarchy, a classification system for formal languages, and explore the applications of automata theory in computer science, including lexical analysis and parsing. If you like this book, write a review!
Engineering Trustworthy Software Systems
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Author : Jonathan P. Bowen
language : en
Publisher: Springer Nature
Release Date : 2025-04-04
Engineering Trustworthy Software Systems written by Jonathan P. Bowen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-04 with Computers categories.
This book PSE 15584 constitutes the refereed proceedings of the 6th International School on Engineering Trustworthy Software Systems, SETSS 2024, held in Chongqing, China, in April 14-21, 2024. The 5 full papers and 2 short papers were carefully reviewed and selected from 7 submissions. The proceedings focuses on -Preparatory Course: Introduction to Mathematical Logic and Logic of Programming; -Introduction to Digital Twins -Theories of Contracts and Their Applications -From Automata Models to Validated BCI-Based Cooperative Control On the Viability of Rigorous Approaches to Human-Cyber-Physical Systems of Systems; What Came First, Math or Computing? -What Came First, Math or Computing? -Software Engineering for Explainable AI -Distribution Testing: The New Frontier for Formal Methods
Volume 5 Algebraic And Logical Structures
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Author : S. Abramsky
language : en
Publisher: OUP Oxford
Release Date : 2001-01-25
Volume 5 Algebraic And Logical Structures written by S. Abramsky and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-25 with Computers categories.
This handbook volume covers fundamental topics of semantics in logic and computation. The chapters (some monographic in length), were written following years of co-ordination and follow a thematic point of view. The volume brings the reader up to front line research, and is indispensable to any serious worker in the areas.
Mathematics Unlimited 2001 And Beyond
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Author : Björn Engquist
language : en
Publisher: Springer
Release Date : 2017-04-05
Mathematics Unlimited 2001 And Beyond written by Björn Engquist and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-05 with Mathematics categories.
This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty.
Mathematics And Computation
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Author : Avi Wigderson
language : en
Publisher: Princeton University Press
Release Date : 2019-10-29
Mathematics And Computation written by Avi Wigderson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-29 with Computers categories.
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 1995
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
A Course In Mathematical Logic For Mathematicians
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Author : Yu. I. Manin
language : en
Publisher: Springer
Release Date : 2012-03-03
A Course In Mathematical Logic For Mathematicians written by Yu. I. Manin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-03 with Mathematics categories.
1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.
Mathematical Methods In Linguistics
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Author : Barbara B.H. Partee
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Methods In Linguistics written by Barbara B.H. Partee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. Forupper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language.
Good Thinking
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Author : Denise D. Cummins
language : en
Publisher: Cambridge University Press
Release Date : 2012-04-16
Good Thinking written by Denise D. Cummins 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 2012-04-16 with History categories.
Do you know what economists mean when they refer to you as a "rational agent"? Or why a psychologist might label your idea a "creative insight"? After reading this book, you will know how the best and brightest thinkers judge the ways we decide, argue, solve problems, and tell right from wrong.
Proceedings Of The Ninth Annual Structure In Complexity Theory Conference
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Author : IEEE Computer Society. Technical Committee on Mathematical Foundations of Computing
language : en
Publisher:
Release Date : 1994
Proceedings Of The Ninth Annual Structure In Complexity Theory Conference written by IEEE Computer Society. Technical Committee on Mathematical Foundations of Computing and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Computational complexity categories.