Sale!

Forcing with Random Variables and Proof Complexity 1st Edition by Jan Krajicek ISBN 0521154332 9780521154338

Original price was: $50.00.Current price is: $35.00.

Forcing with Random Variables and Proof Complexity 1st Edition Jan Krajíček Digital Instant Download

Author(s): Jan Krajíček
ISBN(s): 9780521154338, 0521154332
Edition: 1
File Details: PDF, 1.12 MB
Year: 2011
Language: english
SKU: EB-2503504 Category: Tag:

Forcing with Random Variables and Proof Complexity 1st Edition by Jan Krajicek – Ebook PDF Instant Download/Delivery: 0521154332, 9780521154338
Full download Forcing with Random Variables and Proof Complexity 1st Edition after payment

Product details:

ISBN 10: 0521154332 
ISBN 13: 9780521154338
Author: Jan Krajicek

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.

Forcing with Random Variables and Proof Complexity 1st Table of contents:

Part I: Foundations of Forcing and Random Variables

  1. Introduction to Forcing

  2. Basic Concepts of Random Variables

  3. Connecting Forcing and Random Variables

  4. Historical Background and Motivations

Part II: Forcing Techniques in Proof Complexity

  1. Forcing in Propositional Proof Systems

  2. Randomized Proof Systems

  3. Applications of Forcing to Lower Bounds

  4. Forcing and Hardness Amplification

Part III: Advanced Topics and Applications

  1. Random Variables in Complexity Theory

  2. Forcing and Circuit Complexity

  3. Constructing Hard Instances via Forcing

  4. Probabilistic Methods in Proof Complexity

Part IV: Open Problems and Future Directions

  1. Challenges in Forcing and Randomized Proofs

  2. Emerging Trends and Research Frontiers

  3. Conclusion and Perspectives

People also search for Forcing with Random Variables and Proof Complexity 1st:

forcing with random variables and proof
    
forcing with random variables and proof complexity
    
how to prove two random variables are independent
    
forcing variables
    
prove two random variables are not independent

Tags: Jan Krajicek, Forcing, Proof Complexity