Skip to main content
Springer Nature Link
Log in

Characterizing prime implicants as projective spaces

  • Conference paper
  • First Online:
Advances in Artificial Intelligence (AI*IA 1993)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 728))

Included in the following conference series:

  • 144 Accesses

Abstract

A new formalization of prime implicants through projective spaces is given. A formula is associated with a matrix over the set {0,1}. Every maximal set of linearly independent rows of such a matrix generates a vector space V. We show that particular projective subspaces associated with the vector subspaces of V correspond to the prime implicants of the formula. This characterization enables the generation of prime implicants as solution set of a system of linear equations with constrains. Such a system is showed to be equivalent to an integer programming problem.

This work has been partially supported by ”Progetto Finalizzato Sistemi informatici e Calcolo Parallelo” of C.N.R.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Dantzig G., Linear Programming and Extensions, Princeton University Press, Princeton, New Jersey, 1963.

    Google Scholar 

  2. Jackson, P. and Pais, J., “Computing Prime Implicants”, Proc. International Conference on Automated Deduction, Lecture Notes on Artificial Intelligence 449, pp. 543–557, 1990.

    Google Scholar 

  3. Mendelson, E., Introduction to Mathematical Logic, Van Nostrand, Princeton, 1964.

    Google Scholar 

  4. Pirri, F. and Pizzuti, C., A geometric method to compute prime implicants, DIS, Technical Report, 1992, Università di Roma “La Sapienza”.

    Google Scholar 

  5. Quine, W. V. O., “The problem of simplifying truth functions”, American Math. Monthly, 59 (1952), 521–531.

    Google Scholar 

  6. Sernesi, E., Geometria1, Boringhieri, 1989.

    Google Scholar 

  7. Slagle, J. R., Chang, C. L. and Lee, R. C. T., “A New algorithm for generating prime implicants”, IEEE Trans. on Comp., 19(4) (1970), 304–310.

    Google Scholar 

  8. Socher, R., “Optimizing the clausal normal form transformation”, Journal of Automated Reasoning, 7 (1991), 325–336.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Universita′ di Roma ‘LaSapienza‘, via Salaria 113, 00198, Roma

    Fiora Pirri

  2. Localita′ S.Stefano, CRAI, 87036, Rende (CS)

    Clara Pizzuti

Authors
  1. Fiora Pirri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Clara Pizzuti
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Pietro Torasso

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pirri, F., Pizzuti, C. (1993). Characterizing prime implicants as projective spaces. In: Torasso, P. (eds) Advances in Artificial Intelligence. AI*IA 1993. Lecture Notes in Computer Science, vol 728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57292-9_40

Download citation

  • DOI: https://doi.org/10.1007/3-540-57292-9_40

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57292-3

  • Online ISBN: 978-3-540-48038-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics