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.
| ISBN: | 9781108416849 |
| Publication date: | 28th March 2019 |
| Author: | Jan Charles University, Prague Krajíek |
| Publisher: | Cambridge University Press |
| Format: | Hardback |
| Pagination: | 530 pages |
| Series: | Encyclopedia of Mathematics and its Applications |
| Genres: |
Mathematical logic Maths for computer scientists Artificial intelligence |
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.
Proof Complexity features in the following genres: Mathematical logic, Maths for computer scientists, Artificial intelligence
Proof Complexity is available in Hardback
Proof Complexity was written by Jan Charles University, Prague Krajíek and published by Cambridge University Press
Proof Complexity has 530 pages
Yes it is part of Encyclopedia of Mathematics and its Applications series
£132.30