Proof Complexity: 170 (Encyclopedia of Mathematics and its Applications, Series Number 170)

Kraj?cek, Jan

ISBN 10: 1108416845 / ISBN 13: 9781108416849

Published by Cambridge University Press, 2019

About this Item

Seller Inventory # V9781108416849

Bibliographic Details

• Title: Proof Complexity: 170 (Encyclopedia of Mathematics and its Applications, Series Number 170)
• Publisher: Cambridge University Press
• Publication Date: 2019
• Language: English
• ISBN 10: 1108416845
• ISBN 13: 9781108416849
• Binding: Hardcover
• Condition: New

About this title

Synopsis

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.

About the Author

Jan Krajíček is Professor of Mathematical Logic in the Faculty of Mathematics and Physics at Charles University, Prague. He is a member of the Academia Europaea and of the Learned Society of the Czech Republic. He has been an invited speaker at the European Congress of Mathematicians and at the International Congresses of Logic, Methodology and Philosophy of Science.