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Author: Stephen Cook
Publisher: Cambridge University Press
Published: 2010-01-25
Total Pages: 496
ISBN-13: 1139486306
DOWNLOAD EBOOKThis 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.
Author: Pavel Pudlák
Publisher: Springer Science & Business Media
Published: 2013-04-22
Total Pages: 699
ISBN-13: 3319001191
DOWNLOAD EBOOKThe 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.
Author: Jan Krajíček
Publisher: Cambridge University Press
Published: 2019-03-28
Total Pages: 533
ISBN-13: 1108416845
DOWNLOAD EBOOKOffers a self-contained work presenting basic ideas, classical results, current state of the art and possible future directions in proof complexity.
Author: Jan Krajicek
Publisher: Cambridge University Press
Published: 1995-11-24
Total Pages: 361
ISBN-13: 0521452058
DOWNLOAD EBOOKDiscusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.
Author: Stephen Cook
Publisher: Cambridge University Press
Published: 2010-01-25
Total Pages: 496
ISBN-13: 9780521517294
DOWNLOAD EBOOKThis 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.
Author: Alfred North Whitehead
Publisher:
Published: 1910
Total Pages: 688
ISBN-13:
DOWNLOAD EBOOKAuthor: Jean H. Gallier
Publisher: Courier Dover Publications
Published: 2015-06-18
Total Pages: 532
ISBN-13: 0486780821
DOWNLOAD EBOOKThis advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.
Author: Stephen Cook
Publisher:
Published: 2010
Total Pages: 479
ISBN-13: 9780511683633
DOWNLOAD EBOOKA treatise on bounded arithmetic and propositional proof complexity by the leader in the field.
Author: Sanjeev Arora
Publisher: Cambridge University Press
Published: 2009-04-20
Total Pages: 609
ISBN-13: 0521424267
DOWNLOAD EBOOKNew and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author: Matthias Baaz
Publisher: Cambridge University Press
Published: 2011-06-06
Total Pages: 541
ISBN-13: 1139498436
DOWNLOAD EBOOKThis volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.
