Decision Procedures

An Algorithmic Point of View

  • Daniel Kroening
  • Ofer Strichman

Part of the Texts in Theoretical Computer Science book series (TTCS)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Daniel Kroening, Ofer Strichman
    Pages 1-23
  3. Daniel Kroening, Ofer Strichman
    Pages 25-57
  4. Daniel Kroening, Ofer Strichman
    Pages 59-80
  5. Daniel Kroening, Ofer Strichman
    Pages 81-110
  6. Daniel Kroening, Ofer Strichman
    Pages 111-147
  7. Daniel Kroening, Ofer Strichman
    Pages 149-170
  8. Daniel Kroening, Ofer Strichman
    Pages 171-179
  9. Daniel Kroening, Ofer Strichman
    Pages 181-206
  10. Daniel Kroening, Ofer Strichman
    Pages 207-224
  11. Daniel Kroening, Ofer Strichman
    Pages 225-239
  12. Daniel Kroening, Ofer Strichman
    Pages 241-268
  13. Back Matter
    Pages 269-304

About this book


A decision procedure is an algorithm that, given a decision problem, terminates with a correct yes/no answer. Here, the authors focus on theories that are expressive enough to model real problems, but are still decidable. Specifically, the book concentrates on decision procedures for first-order theories that are commonly used in automated verification and reasoning, theorem-proving, compiler optimization and operations research. The techniques described in the book draw from fields such as graph theory and logic, and are routinely used in industry.

The authors introduce the basic terminology of satisfiability modulo theories and then, in separate chapters, study decision procedures for each of the following theories: propositional logic; equalities and uninterpreted functions; linear arithmetic; bit vectors; arrays; pointer logic; and quantified formulas. They also study the problem of deciding combined theories and dedicate a chapter to modern techniques based on an interplay between a SAT solver and a decision procedure for the investigated theory.

This textbook has been used to teach undergraduate and graduate courses at ETH Zurich, at the Technion, Haifa, and at the University of Oxford. Each chapter includes a detailed bibliography and exercises. Lecturers' slides and a C++ library for rapid prototyping of decision procedures are available from the authors' website.


Algorithms Automat C++ algorithm logic operations research optimization proving verification

Authors and affiliations

  • Daniel Kroening
    • 1
  • Ofer Strichman
    • 2
  1. 1.Computing LaboratoryUniversity of OxfordOxfordUnited Kingdom
  2. 2.William Davidson Faculty of Industrial Engineering and ManagementTechnion – Israel Institute of TechnologyTechnion CityIsrael

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science
  • Print ISBN 978-3-540-74104-6
  • Online ISBN 978-3-540-74105-3
  • Series Print ISSN 1862-4499
  • Buy this book on publisher's site
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