Skip to main content
SpringerLink
Log in

A Linear Time Algorithm for Recognizing Regular Boolean Functions

  • Conference paper
  • First Online:
Algorithms and Computation (ISAAC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1741))

Included in the following conference series:

  • 617 Accesses

Abstract

A positive (or monotone) Boolean function is regular if its variables are naturally ordered, left to right, by decreasing strength, so that shifting the non-zero component of any true vector to the left always yields another true vector. In this paper, we propose a simple linear time algorithm to recognize whether a positive function is regular.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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.

References

  1. H. Aizenstein, T. Hegedus, L. Hellerstein and L. Pitt, Complexity theoretic hardness results for query learning, Computational Complexity, 7 (1998) 19–53.

    Google Scholar 

  2. M. O. Ball and J. S. Provan, Disjoint products and efficient computation of reliability, Operations Research, 36 (1988) 703–715.

    Google Scholar 

  3. P. Bertolazzi and A. Sassano, An O(mn) time algorithm for regular set-covering problems, Theoretical Computer Science, 54 (1987) 237–247.

    Google Scholar 

  4. E. Boros, P. L. Hammer, T. Ibaraki and K. Kawakami, Polynomial time recognition of 2-monotonic positive Boolean functions given by an oracle, SIAM J. Computing, 26 (1997) 93–109.

    Google Scholar 

  5. V. Chvátal and P. L. Hammer, Aggregation of inequalities in integer programming, Annals of Discrete Mathematics, 1 (1977) 145–162.

    Google Scholar 

  6. Y. Crama, Dualization of regular Boolean functions, Discrete Applied Mathematics, 16 (1987) 79–85.

    Google Scholar 

  7. N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica, 4 (1984) 373–396.

    Google Scholar 

  8. L. G. Khachiyan, A polynomial algorithm in linear programming, Soviet Mathematics Doklady, 20 (1979) 191–194.

    Google Scholar 

  9. K. Makino and T. Ibaraki, The maximum latency and identification of positive Boolean functions, SIAM Journal on Computing, 26 (1997) 1363–1383.

    Google Scholar 

  10. K. Makino and T. Ibaraki, A fast and simple algorithm for identifying 2-monotonic positive Boolean functions, Journal of Algorithms, 26 (1998) 291–305.

    Google Scholar 

  11. K. Makino, A linear time algorithm for recognizing regular Boolean functions, RUTCOR Research Report RRR 32-98, Rutgers University 1998.

    Google Scholar 

  12. S. Muroga, “Threshold Logic and Its Applications,” Wiley-Interscience, 1971.

    Google Scholar 

  13. U. N. Peled and B. Simeone, Polynomial-time algorithm for regular set-covering and threshold synthesis, Discrete Applied Mathematics, 12 (1985) 57–69.

    Google Scholar 

  14. J. S. Provan and M. O. Ball, Efficient recognition of matroids and 2-monotonic systems, in “Applications of Discrete Mathematics,” (R. Ringeisen and F. Roberts, Eds.), pp. 122–134, SIAM, Philadelphia, 1988.

    Google Scholar 

  15. R. O. Winder, “Threshold Logic,” Doctoral dissertation, Mathematics Department, Princeton University, 1962.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Systems and Human Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, 560, Japan

    Kazuhisa Makino

Authors
  1. Kazuhisa Makino
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Makino, K. (1999). A Linear Time Algorithm for Recognizing Regular Boolean Functions. In: Algorithms and Computation. ISAAC 1999. Lecture Notes in Computer Science, vol 1741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46632-0_27

Download citation

  • DOI: https://doi.org/10.1007/3-540-46632-0_27

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66916-6

  • Online ISBN: 978-3-540-46632-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation