Skip to content

Your Cambridge account can now be used to log into other Cambridge products and services including Cambridge One, Cambridge LMS, Cambridge GO and Cambridge Dictionary Plus

Register Sign in Wishlist

Logical Foundations of Proof Complexity

  • Date Published: March 2014
  • availability: Available
  • format: Paperback
  • isbn: 9781107694118


Add to wishlist

Other available formats:
Hardback, eBook

Looking for an inspection copy?

Please email to enquire about an inspection copy of this book

Product filter button
About the Authors
  • 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 complexity classes range from AC0 for the weakest theory up to the polynomial hierarchy. Each bounded theorem in a theory translates into a family of (quantified) propositional tautologies with polynomial size proofs in the corresponding proof system. The theory proves the soundness of the associated 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.

    • Suitable as an advanced graduate text
    • Contains a wealth of original material
    • Will serve as a valuable reference for proof complexity
    Read more

    Reviews & endorsements

    'The book under review is a comprehensive introduction to bounded arithmetic … While the book is primarily aimed at students and researchers with background in theoretical computer science, its prerequisites in computational complexity are rather mild and are summarized in the Appendix, thus the book should be easily accessible to logicians and mathematicians coming from a different background. Some familiarity with logic will help the reader, but in this respect the book is more or less self-contained, the relevant bits of proof theory and model theory are developed in the first chapters in detail.' Zentralblatt MATH

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: March 2014
    • format: Paperback
    • isbn: 9781107694118
    • length: 496 pages
    • dimensions: 234 x 156 x 28 mm
    • weight: 0.76kg
    • contains: 17 b/w illus. 5 tables
    • availability: Available
  • Table of Contents

    1. Introduction
    2. The predicate calculus and the system
    3. Peano arithmetic and its subsystems
    4. Two-sorted logic and complexity classes
    5. The theory V0 and AC0
    6. The theory V1 and polynomial time
    7. Propositional translations
    8. Theories for polynomial time and beyond
    9. Theories for small classes
    10. Proof systems and the reflection principle
    11. Computation models.

  • Authors

    Stephen Cook, University of Toronto
    Stephen Cook is a professor at the University of Toronto. He is author of many research papers, including his famous 1971 paper 'The Complexity of Theorem Proving Procedures', and the 1982 recipient of the Turing Award. He was awarded a Steacie Fellowship in 1977 and a Killam Research Fellowship in 1982 and received the CRM/Fields Institute Prize in 1999. He is a Fellow of the Royal Society of London and the Royal Society of Canada and was elected to membership in the National Academy of Sciences (United States) and the American Academy of Arts and Sciences.

    Phuong Nguyen, McGill University, Montréal
    Phuong Nguyen (Nguyễn Thế Phương) received his MSc and PhD degrees from University of Toronto in 2004 and 2008 respectively. He has been awarded postdoctoral fellowships by the Eduard Čech Center for Algebra and Geometry (the Czech Republic) for 2008–9, and by the Natural Sciences and Engineering Research Council of Canada (NSERC), effective September 2009.

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.