Logical Foundations Of Proof Complexity PDF Download
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| Author | : Stephen Cook |
| Publisher | : Cambridge University Press |
| Total Pages | : 496 |
| Release | : 2010-01-25 |
| Genre | : Mathematics |
| ISBN | : 1139486306 |
Download Logical Foundations of Proof Complexity Book 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.
| Author | : Stephen Cook |
| Publisher | : Cambridge University Press |
| Total Pages | : 496 |
| Release | : 2010-01-25 |
| Genre | : Mathematics |
| ISBN | : 9780521517294 |
Download Logical Foundations of Proof Complexity Book 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.
| Author | : Stephen Cook |
| Publisher | : |
| Total Pages | : 479 |
| Release | : 2010 |
| Genre | : Computational complexity |
| ISBN | : 9780511683633 |
Download Perspectives in Logic Book in PDF, ePub and Kindle
A treatise on bounded arithmetic and propositional proof complexity by the leader in the field.
| Author | : Pavel Pudlák |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 699 |
| Release | : 2013-04-22 |
| Genre | : Mathematics |
| ISBN | : 3319001191 |
Download Logical Foundations of Mathematics and Computational Complexity Book 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.
| Author | : Jan Krajíček |
| Publisher | : Cambridge University Press |
| Total Pages | : 533 |
| Release | : 2019-03-28 |
| Genre | : Mathematics |
| ISBN | : 1108266126 |
Download Proof Complexity Book in PDF, ePub and Kindle
Proof complexity is a rich subject drawing on methods from logic, combinatorics, algebra and computer science. This self-contained book presents the basic concepts, classical results, current state of the art and possible future directions in the field. It stresses a view of proof complexity as a whole entity rather than a collection of various topics held together loosely by a few notions, and it favors more generalizable statements. Lower bounds for lengths of proofs, often regarded as the key issue in proof complexity, are of course covered in detail. However, upper bounds are not neglected: this book also explores the relations between bounded arithmetic theories and proof systems and how they can be used to prove upper bounds on lengths of proofs and simulations among proof systems. It goes on to discuss topics that transcend specific proof systems, allowing for deeper understanding of the fundamental problems of the subject.
| Author | : Alfred North Whitehead |
| Publisher | : |
| Total Pages | : 696 |
| Release | : 1910 |
| Genre | : Logic, Symbolic and mathematical |
| ISBN | : |
Download Principia Mathematica Book in PDF, ePub and Kindle
| Author | : Jean H. Gallier |
| Publisher | : Courier Dover Publications |
| Total Pages | : 532 |
| Release | : 2015-06-18 |
| Genre | : Mathematics |
| ISBN | : 0486780821 |
Download Logic for Computer Science Book in PDF, ePub and Kindle
This 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 | : Jan Krajicek |
| Publisher | : Cambridge University Press |
| Total Pages | : 361 |
| Release | : 1995-11-24 |
| Genre | : Computers |
| ISBN | : 0521452058 |
Download Bounded Arithmetic, Propositional Logic and Complexity Theory Book in PDF, ePub and Kindle
Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.
| Author | : Sanjeev Arora |
| Publisher | : Cambridge University Press |
| Total Pages | : 609 |
| Release | : 2009-04-20 |
| Genre | : Computers |
| ISBN | : 0521424267 |
Download Computational Complexity Book in PDF, ePub and Kindle
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
| Author | : André Platzer |
| Publisher | : Springer |
| Total Pages | : 639 |
| Release | : 2018-07-30 |
| Genre | : Mathematics |
| ISBN | : 3319635883 |
Download Logical Foundations of Cyber-Physical Systems Book in PDF, ePub and Kindle
Cyber-physical systems (CPSs) combine cyber capabilities, such as computation or communication, with physical capabilities, such as motion or other physical processes. Cars, aircraft, and robots are prime examples, because they move physically in space in a way that is determined by discrete computerized control algorithms. Designing these algorithms is challenging due to their tight coupling with physical behavior, while it is vital that these algorithms be correct because we rely on them for safety-critical tasks. This textbook teaches undergraduate students the core principles behind CPSs. It shows them how to develop models and controls; identify safety specifications and critical properties; reason rigorously about CPS models; leverage multi-dynamical systems compositionality to tame CPS complexity; identify required control constraints; verify CPS models of appropriate scale in logic; and develop an intuition for operational effects. The book is supported with homework exercises, lecture videos, and slides.
