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Space in Weak Propositional Proof Systems

  • Ilario Bonacina

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Ilario Bonacina
    Pages 1-12
  3. General Results and Techniques

    1. Front Matter
      Pages 13-13
    2. Ilario Bonacina
      Pages 15-28
    3. Ilario Bonacina
      Pages 29-40
    4. Ilario Bonacina
      Pages 41-57
  4. Applications

    1. Front Matter
      Pages 59-59
    2. Ilario Bonacina
      Pages 61-69
    3. Ilario Bonacina
      Pages 71-88
    4. Ilario Bonacina
      Pages 89-101
  5. A Postlude

    1. Front Matter
      Pages 103-103
  6. Back Matter
    Pages 119-130

About this book

Introduction

This book considers logical proof systems from the point of view of their space complexity. After an introduction to propositional proof complexity the author structures the book into three main parts. Part I contains two chapters on resolution, one containing results already known in the literature before this work and one focused on space in resolution, and the author then moves on to polynomial calculus and its space complexity with a focus on the combinatorial technique to prove monomial space lower bounds. The first chapter in Part II addresses the proof complexity and space complexity of the pigeon principles. Then there is an interlude on a new type of game, defined on bipartite graphs, essentially independent from the rest of the book, collecting some results on graph theory. Finally Part III analyzes the size of resolution proofs in connection with the Strong Exponential Time Hypothesis (SETH) in complexity theory.

The book is appropriate for researchers in theoretical computer science, in particular computational complexity.

Keywords

Proof Complexity Mathematical Logic Polynomial Calculus System Proof System Resolution System Satisfiability

Authors and affiliations

  • Ilario Bonacina
    • 1
  1. 1.Dept. Ciències de la ComputacióUniversitat Politècnica de CatalunyaBarcelonaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-73453-8
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-319-73452-1
  • Online ISBN 978-3-319-73453-8
  • Buy this book on publisher's site
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