Skip to main content

Complexity Measures and Reductions

  • Chapter
Introduction to Circuit Complexity

Part of the book series: Texts in Theoretical Computer Science An EATCS Series ((TTCS))

  • 651 Accesses

Abstract

Suppose we are given two binary strings, each consisting of n bits, a = a n−1 a n−2 ... a 0, and b = b n−1 b n−2 ... b 0. We want to solve the following problem: Interpret a and b as binary representations of two natural numbers and compute their sum (again in binary). We refer to this problem as ADD.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 84.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographic Remarks

  1. C. Shannon. The synthesis of two-terminal switching circuits. Bell Systems Technical Journal, 28: 59–98, 1949.

    MathSciNet  MATH  Google Scholar 

  2. O. B. Lupanov. A method of circuit synthesis. Izvestia VUZ Radiofizika, 1: 120–140, 1958.

    Google Scholar 

  3. J. E. Savage. The Complexity of Computing. John Wiley & Sons, New York, 1976.

    MATH  Google Scholar 

  4. M. J. Fischer. Lectures on network complexity. Universität Frankfurt/Main, 1974.

    Google Scholar 

  5. H. Straubing. Finite Automata, Formal Logic, and Circuit Complexity. Birkhäuser, Boston, MA, 1994.

    Book  MATH  Google Scholar 

  6. A. K. Chandra, L. Stockmeyer, and U. Vishkin. Constant depth reducibility. SIAM Journal on Computing, 13: 423–439, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  7. I. Wegener. The Complexity of Boolean Functions. WileyTeubner series in computer science. B. G. Teubner & John Wiley, Stuttgart, 1987.

    Google Scholar 

  8. I. Wegener. Effiziente Algorithmen fur grundlegende Funktionen. Leitfäden und Monographien der Informatik. B. G. Teubner, Stuttgart, 1989.

    Google Scholar 

  9. C. Wilson. Relativized NC. Mathematical Systems Theory, 20: 13–29, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  10. U. Schöning. Complexity and Structure. Lecture Notes in Com- puter Science 211, Springer-Verlag, Berlin, 1986.

    Google Scholar 

  11. A. K. Chandra, L. Stockmeyer, and U. Vishkin. Constant depth reducibility. SIAM Journal on Computing, 13: 423–439, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  12. P. W. Beame, S. A. Cook, and H. J. Hoover. Log depth circuits for division and related problems. SIAM Journal on Computing, 15: 994–1003, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  13. I. Wegener. The Complexity of Boolean Functions. WileyTeubner series in computer science. B. G. Teubner and John Wiley, Stuttgart, 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Vollmer, H. (1999). Complexity Measures and Reductions. In: Introduction to Circuit Complexity. Texts in Theoretical Computer Science An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03927-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-03927-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08398-3

  • Online ISBN: 978-3-662-03927-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics