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Author : Richard Statman
Publisher :
ISBN 13 :
Total Pages : 246 pages
Book Rating : 4.:/5 (123 download)
Download or read book Structural Complexity of Proofs written by Richard Statman and published by . This book was released on 1974 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jose L. Balcazar
Publisher : Springer Science & Business Media
ISBN 13 : 3642970621
Total Pages : 201 pages
Book Rating : 4.6/5 (429 download)
Download or read book Structural Complexity I written by Jose L. Balcazar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the achievement of a fonnal definition of the concept of "algorithm", the Mathematical Theory of Computation has developed into a broad and rich discipline. The notion of "complexity of an algorithm" yields an important area of research, known as Complexity Theory, that can be approached from several points of view. Some of these are briefly discussed in the Introduction and, in particular, our view of the "Structural" approach is outlined there. We feel the subject is mature enough to permit collecting and interrelating many of the results in book fonn. Let us point out that a substantial part of the knowledge in Structural Complexity Theory can be found only in specialized journals, symposia proceedings, and monographs like doctoral dissertations or similar texts, mostly unpublished. We believe that a task to be done soon is a systematization of the interconnections between all the research lines; this is a serious and long task. We hope that the two volumes of this book can serve as a starting point for this systematization process.
Author : Jose L. Balcazar
Publisher : Springer
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.:/5 (318 download)
Download or read book Structural Complexity I written by Jose L. Balcazar and published by Springer. This book was released on 1995 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first volume of a systematic two-volume presentation of the various areas of research on structural complexity. This book presents the basic concepts of structural complexity, providing the background necessary for an understanding of complexity theory. It will be invaluable to individuals who would like a better understanding of basic concepts.
Author : Jose L. Balcazar
Publisher : Springer Science & Business Media
ISBN 13 : 3642792359
Total Pages : 223 pages
Book Rating : 4.6/5 (427 download)
Download or read book Structural Complexity I written by Jose L. Balcazar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the six years since the first edition of this book was published, the field of Structural Complexity has grown quite a bit. However, we are keeping this volume at the same basic level that it had in the first edition, and the only new result incorporated as an appendix is the closure under complementation of nondeterministic space classes, which in the previous edition was posed as an open problem. This result was already included in our Volume II, but we feel that due to the basic nature of the result, it belongs to this volume. There are of course other important results obtained during these last six years. However, as they belong to new areas opened in the field they are outside the scope of this fundamental volume. Other changes in this second edition are the update of some Bibliograph ical Remarks and references, correction of many mistakes and typos, and a renumbering of the definitions and results. Experience has shown us that this new numbering is a lot more friendly, and several readers have confirmed this opinion. For the sake of the reader of Volume II, where all references to Volume I follow the old numbering, we have included here a table indicating the new number corresponding to each of the old ones.
Author : José Luis Balcázar
Publisher :
ISBN 13 :
Total Pages : 306 pages
Book Rating : 4.3/5 (91 download)
Download or read book Structural Complexity written by José Luis Balcázar and published by . This book was released on 1988 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jose L. Balcazar
Publisher : Springer Science & Business Media
ISBN 13 : 3642753574
Total Pages : 295 pages
Book Rating : 4.6/5 (427 download)
Download or read book Structural Complexity II written by Jose L. Balcazar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of a two volume collection on Structural Complexity. This volume assumes as a prerequisite knowledge about the topics treated in Volume I, but the present volume itself is nearly self-contained. As in Volume I, each chapter of this book ends with a section entitled "Bibliographical Remarks", in which the relevant references for the chapter are briefly commented upon. These sections might also be of interest to those wanting an overview of the evolution of the field, as well as relevant related results which are not included in the text. Each chapter includes a section of exercises. The reader is encouraged to spend some time on them. Some results presented as exercises are occasionally used later in the text. A reference is provided for the most interesting and for the most useful exercises. Some exercises are marked with a • to indicate that, to the best knowledge of the authors, the solution has a certain degree of difficulty. Many topics from the field of Structural Complexity are not treated in depth, or not treated at all. The authors bear all responsibility for the choice of topics, which has been made based on the interest of the authors on each topic. Many friends and colleagues have made suggestions or corrections. In partic ular we would like to express our gratitude to Richard Beigel, Ron Book, Rafael Casas, Jozef Gruska, Uwe Schoning, Pekka Orponen, and Osamu Watanabe.
Author : Jan Krajíček
Publisher : Cambridge University Press
ISBN 13 : 1108266126
Total Pages : 533 pages
Book Rating : 4.1/5 (82 download)
Download or read book Proof Complexity written by Jan Krajíček and published by Cambridge University Press. This book was released on 2019-03-28 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Stephen Cook
Publisher : Cambridge University Press
ISBN 13 : 1139486306
Total Pages : 496 pages
Book Rating : 4.1/5 (394 download)
Download or read book Logical Foundations of Proof Complexity written by Stephen Cook and published by Cambridge University Press. This book was released on 2010-01-25 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : J. Kobler
Publisher : Springer Science & Business Media
ISBN 13 : 1461203333
Total Pages : 168 pages
Book Rating : 4.4/5 (612 download)
Download or read book The Graph Isomorphism Problem written by J. Kobler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, a variety ofresults on the complexitystatusofthegraph isomorphism problem has been obtained. These results belong to the so-called structural part of Complexity Theory. Our idea behind this book is to summarize such results which might otherwise not be easily accessible in the literature, and also, to give the reader an understanding of the aims and topics in Structural Complexity Theory, in general. The text is basically self contained; the only prerequisite for reading it is some elementary knowledge from Complexity Theory and Probability Theory. It can be used to teach a seminar or a monographic graduate course, but also parts of it (especially Chapter 1) provide a source of examples for a standard graduate course on Complexity Theory. Many people have helped us in different ways III the process of writing this book. Especially, we would like to thank V. Arvind, R.V. Book, E. May ordomo, and the referee who gave very constructive comments. This book project was especially made possible by a DAAD grant in the "Acciones In tegrada" program. The third author has been supported by the ESPRIT project ALCOM-II.
Author : Michael L. O'Leary
Publisher :
ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Structure of Proof written by Michael L. O'Leary and published by . This book was released on 2002 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a one-semester freshman or sophomore level course on the fundamentals of proof writing or transition to advanced mathematics course. Rather than teach mathematics and the structure of proofs simultaneously, this text first introduces logic as the foundation of proofs and then demonstrates how logic applies to mathematical topics. This method ensures that the students gain a firm understanding of how logic interacts with mathematics and empowers them to solve more complex problems in future math courses.
Author : Sanjeev Arora
Publisher : Cambridge University Press
ISBN 13 : 0521424267
Total Pages : 609 pages
Book Rating : 4.5/5 (214 download)
Download or read book Computational Complexity written by Sanjeev Arora and published by Cambridge University Press. This book was released on 2009-04-20 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author : Jan Krajíček
Publisher : Cambridge University Press
ISBN 13 : 1108416845
Total Pages : 533 pages
Book Rating : 4.1/5 (84 download)
Download or read book Proof Complexity written by Jan Krajíček and published by Cambridge University Press. This book was released on 2019-03-28 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers 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
ISBN 13 : 0521452058
Total Pages : 361 pages
Book Rating : 4.5/5 (214 download)
Download or read book Bounded Arithmetic, Propositional Logic and Complexity Theory written by Jan Krajicek and published by Cambridge University Press. This book was released on 1995-11-24 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.
Author : Sara Negri
Publisher : Cambridge University Press
ISBN 13 : 9780521793070
Total Pages : 276 pages
Book Rating : 4.7/5 (93 download)
Download or read book Structural Proof Theory written by Sara Negri and published by Cambridge University Press. This book was released on 2001-06-18 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics, and computer science. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated.
Author : Jan Krajíček
Publisher : Cambridge University Press
ISBN 13 : 1139493922
Total Pages : 265 pages
Book Rating : 4.1/5 (394 download)
Download or read book Forcing with Random Variables and Proof Complexity written by Jan Krajíček and published by Cambridge University Press. This book was released on 2010-12-23 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a new approach to building models of bounded arithmetic, with techniques drawn from recent results in computational complexity. Propositional proof systems and bounded arithmetics are closely related. In particular, proving lower bounds on the lengths of proofs in propositional proof systems is equivalent to constructing certain extensions of models of bounded arithmetic. This offers a clean and coherent framework for thinking about lower bounds for proof lengths, and it has proved quite successful in the past. This book outlines a brand new method for constructing models of bounded arithmetic, thus for proving independence results and establishing lower bounds for proof lengths. The models are built from random variables defined on a sample space which is a non-standard finite set and sampled by functions of some restricted computational complexity. It will appeal to anyone interested in logical approaches to fundamental problems in complexity theory.
Author : Paolo Mancosu
Publisher : Oxford University Press
ISBN 13 : 0192895931
Total Pages : 431 pages
Book Rating : 4.1/5 (928 download)
Download or read book An Introduction to Proof Theory written by Paolo Mancosu and published by Oxford University Press. This book was released on 2021 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.
Author : Larry Gerstein
Publisher : Springer Science & Business Media
ISBN 13 : 1468467085
Total Pages : 355 pages
Book Rating : 4.4/5 (684 download)
Download or read book Introduction · to Mathematical Structures and · Proofs written by Larry Gerstein and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper division instructors feel the need to start their courses with the rudiments of logic, set theory, equivalence relations, and other basic mathematical raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried the students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a nontrivial level if they are to achieve the sophisticated blend of knowledge, disci pline, and creativity that we call "mathematical maturity. " I don't believe that "theorem-proving" can be taught any more than "question-answering" can be taught. Nevertheless, I have found that it is possible to guide stu dents gently into the process of mathematical proof in such a way that they become comfortable with the experience and begin asking them selves questions that will lead them in the right direction.
