TY  - BOOK
AU  - Kraj�i�cek,Jan
TI  - Proof complexity
T2  - Encyclopedia of mathematics and its applications
SN  - 9781108271585
AV  - QA9.54 .K72 2019
U1  - 511.3/6 23
PY  - 2019///
CY  - Cambridge, United Kingdom, New York, NY, USA
PB  - Cambridge University Press
KW  - Proof theory
KW  - Computational complexity
KW  - MATHEMATICS / General
KW  - bisacsh
KW  - Electronic books
N1  - Includes bibliographical references and index
N2  - 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
UR  - https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=2046158
ER  -