Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Books
  3. Bounded Arithmetic, Propositional Logic and Complexity Theory
  • Cited by 218
  • Jan Krajicek, Academy of Sciences of the Czech Republic, Prague
Publisher:
Cambridge University Press
Online publication date:
December 2009
Print publication year:
1995
Online ISBN:
9780511529948
DOI:
https://doi.org/10.1017/CBO9780511529948
Subjects:
Mathematics (general), Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Logic, Categories and Sets, Computer Science
Series:
Encyclopedia of Mathematics and its Applications (60)
Information

Book description

This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then treated, including polynomial simulations and conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, direct independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the method of Boolean valuations, the issue of hard tautologies and optimal proof systems, combinatorics and complexity theory within bounded arithmetic, and relations to complexity issues of predicate calculus. Students and researchers in mathematical logic and complexity theory will find this comprehensive treatment an excellent guide to this expanding interdisciplinary area.

Reviews

‘This interesting book provides a brisk account of current research in bounded arithmetic and the complexity of propositional logic.’

Source: Mathematika

‘It can be strongly recommended especially to mathematicians and computer scientists working in the field and to graduate students.’

Source: European Mathematical Society Newsletter

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Contents

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.