© 2017

Space in Weak Propositional Proof Systems


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


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.


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

Authors and affiliations

  1. 1.Dept. Ciències de la ComputacióUniversitat Politècnica de CatalunyaBarcelonaSpain

About the authors

Ilario Bonacina did his PhD at the Computer Science Department at Sapienza Università di Roma under the supervision of Nicola Galesi. After a postdoc in the Theoretical Computer Science Group at KTH Royal Institute of Technology (Stockholm), he is currently a postdoc in the Computer Science Department at Universitat Politècnica de Catalunya (Barcelona). His research interests include computational complexity and mathematical logic.

Bibliographic information

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