Logical Foundations of Mathematics and Computational Complexity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Logical Foundations of Mathematics and Computational Complexity write by Pavel Pudlák. This book was released on 2013-04-22. Logical Foundations of Mathematics and Computational Complexity available in PDF, EPUB and Kindle. The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.
Logical Foundations of Proof Complexity
Logical Foundations of Proof Complexity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Logical Foundations of Proof Complexity write by Stephen Cook. This book was released on 2010-01-25. Logical Foundations of Proof Complexity available in PDF, EPUB and Kindle. This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. The result is a uniform treatment of many systems in the literature.
Logic and Complexity
Logic and Complexity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Logic and Complexity write by Richard Lassaigne. This book was released on 2012-12-06. Logic and Complexity available in PDF, EPUB and Kindle. Logic and Complexity looks at basic logic as it is used in Computer Science, and provides students with a logical approach to Complexity theory. With plenty of exercises, this book presents classical notions of mathematical logic, such as decidability, completeness and incompleteness, as well as new ideas brought by complexity theory such as NP-completeness, randomness and approximations, providing a better understanding for efficient algorithmic solutions to problems. Divided into three parts, it covers: - Model Theory and Recursive Functions - introducing the basic model theory of propositional, 1st order, inductive definitions and 2nd order logic. Recursive functions, Turing computability and decidability are also examined. - Descriptive Complexity - looking at the relationship between definitions of problems, queries, properties of programs and their computational complexity. - Approximation - explaining how some optimization problems and counting problems can be approximated according to their logical form. Logic is important in Computer Science, particularly for verification problems and database query languages such as SQL. Students and researchers in this field will find this book of great interest.
Logical Foundations of Proof Complexity
Logical Foundations of Proof Complexity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Logical Foundations of Proof Complexity write by Stephen Cook. This book was released on 2010-01-25. Logical Foundations of Proof Complexity available in PDF, EPUB and Kindle. This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P.
Logical Foundations of Computer Science
Logical Foundations of Computer Science - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Logical Foundations of Computer Science write by Sergei Artemov. This book was released on 2013-01-05. Logical Foundations of Computer Science available in PDF, EPUB and Kindle. This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2013, held in San Diego, CA, USA in January 2013. The volume presents 29 revised refereed papers carefully selected by the program committee. The scope of the Symposium is broad and includes constructive mathematics and type theory; logic, automata and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logic; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple agent system logics; logics of proof and justification; nonmonotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; and other logics in computer science.
