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Computability and Complexity Theory

  • Steven Homer
  • Alan L. Selman
Textbook

Part of the Texts in Computer Science book series (TCS)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Steven Homer, Alan L. Selman
    Pages 1-21
  3. Steven Homer, Alan L. Selman
    Pages 22-40
  4. Steven Homer, Alan L. Selman
    Pages 41-71
  5. Steven Homer, Alan L. Selman
    Pages 72-77
  6. Steven Homer, Alan L. Selman
    Pages 78-121
  7. Steven Homer, Alan L. Selman
    Pages 122-144
  8. Steven Homer, Alan L. Selman
    Pages 145-180
  9. Back Matter
    Pages 181-195

About this book

Introduction

The theory of computing provides computer science with concepts, models, and formalisms for reasoning about both the resources needed to carry out computa­ tions and the efficiency of the computations that use these resources. lt provides tools to measure the difficulty of combinatorial problems both absolutely and in comparison with other problems. Courses in this subject help students gain an­ alytic skills and enable them to recognize the limits of computation. For these reasons, a course in the theory of computing is usually required in the graduate computer science curriculum. The barder question to address is which topics such a course should cover. We believe that students should learn the fundamental models of computation, the limitations of computation, and the distinctions between feasible and intractable. In particular, the phenomena ofNP-completeness and NP-hardness have pervaded much of science and transformed computer science. One option is to survey a large nurober of theoretical subjects, typically focusing on automata and formal languages. However, these subjects are less important to theoretical computer sci­ ence, and to computer science as a whole, now than in the past. Many students have taken such a course as part of their undergraduate education. We chose not to take that route because computability and complexity theory are the subjects that we feel deeply about and that we believe are important for students to learn. Furthermore, a graduate course should be scholarly. lt is better to treat important topics thoroughly than to survey the field.

Keywords

Automat automata automata theory complexity complexity theory computability theory computer computer science formal language formal languages logic number theory

Authors and affiliations

  • Steven Homer
    • 1
  • Alan L. Selman
    • 2
  1. 1.Department of Computer ScienceBoston UniversityBostonUSA
  2. 2.Department of Computer Science and EngineeringUniversity at BuffaloBuffaloUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3544-4
  • Copyright Information Springer-Verlag New York 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2865-8
  • Online ISBN 978-1-4757-3544-4
  • Series Print ISSN 1868-0941
  • Series Online ISSN 1868-095X
  • Buy this book on publisher's site