Forcing with Random Variables and Proof Complexity
eBook - PDF

Forcing with Random Variables and Proof Complexity

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Forcing with Random Variables and Proof Complexity

About this book

This book introduces a new approach to building models of bounded arithmetic, with techniques drawn from recent results in computational complexity. Propositional proof systems and bounded arithmetics are closely related. In particular, proving lower bounds on the lengths of proofs in propositional proof systems is equivalent to constructing certain extensions of models of bounded arithmetic. This offers a clean and coherent framework for thinking about lower bounds for proof lengths, and it has proved quite successful in the past. This book outlines a brand new method for constructing models of bounded arithmetic, thus for proving independence results and establishing lower bounds for proof lengths. The models are built from random variables defined on a sample space which is a non-standard finite set and sampled by functions of some restricted computational complexity. It will appeal to anyone interested in logical approaches to fundamental problems in complexity theory.

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Yes, you can access Forcing with Random Variables and Proof Complexity by Jan Krajíček in PDF and/or ePUB format, as well as other popular books in Mathematics & Logic in Mathematics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Dedication
  5. Contents
  6. Preface
  7. Acknowledgment
  8. Introduction
  9. Part I Basics
  10. Part II Second-order structures
  11. Part III AC0 world
  12. Part IV AC0(2) world
  13. Part V Towards proof complexity
  14. Part VI Proof complexity of Fd and Fd(⊕)
  15. Part VII Polynomial-time and higher worlds
  16. Part VIII Proof complexity of EF and beyond
  17. Appendix: Non-standard models and the ultrapower
  18. Standard notation, conventions and list of symbols
  19. References
  20. Subject Index
  21. Name Index