Skip to main content

New bounds on formula size

  • Hauptvorträge
  • Conference paper
  • First Online:
Theoretical Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 48))

Abstract

A variety of theorems bounding the formula size of rather simple Boolean functions are described here for the first time. The principal results are improved lower and upper bounds for symmetric functions.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.J. Fischer, A.R. Meyer and M.S. Paterson. "Lower bounds on the size of Boolean formulas: preliminary report", Proc. 7th Ann. ACM Symp. on Th. of Computing (1975), 45–49.

    Google Scholar 

  2. L.H. Harper and J.E. Savage. "On the complexity of the marriage problem", Advances in Mathematics 9, 3 (1972), 299–312.

    Article  Google Scholar 

  3. L. Hodes. "The logical complexity of geometric properties in the plane", J. ACM 17, 2 (1970), 339–347.

    Article  Google Scholar 

  4. L. Hodes and E. Specker. "Lengths of formulas and elimination of quantifiers I", in Contributions to Mathematical Logic, K. Schutte, ed., North Holland Publ. Co., (1968), 175–188.

    Google Scholar 

  5. G. Hotz. "Untere Schranken für das Analyseproblem kontext-freier Sprachen", Techn. Bericht, Univ. des Saarlandes, 1976.

    Google Scholar 

  6. L.S. Khasin. "Complexity bounds for the realization of monotone symmetrical functions by means of formulas in the basis ⋁, &, ⌜.", Eng. trans. in Soviet Physics Dokl., 14 12 (1970), 1149–1151; orig. Dokl. Akad. Nauk SSSR, 189, 4 (1969), 752–755.

    Google Scholar 

  7. B.M. Kloss. "Estimates of the complexity of solutions of systems of linear equations", Eng. trans. in Soviet Math Dokl. 7, 6 (1966), 1537–1540; orig. Dokl. Akad. Nauk SSSR, 171, 4 (1966), 781–783.

    Google Scholar 

  8. W.F. McColl. "Some results on circuit depth", Ph.D. dissertation, Computer Science Dept., Warwick University, 1976.

    Google Scholar 

  9. K. Mehlhorn. "An improved bound on the formula complexity of context-free recognition". Unpublished report, 1976.

    Google Scholar 

  10. E.I. Neciporuk. "A Boolean function", Soviet Math. Dokl. 7, 4 (1966), 999–1000, orig. Dokl. Akad. Nauk SSSR 169, 4 (1966), 765–766.

    Google Scholar 

  11. M.S. Paterson. "An introduction to Boolean function complexity". Stanford Computer Science Report STAN-CS-76-557 Stanford University, 1976; to appear in Astérisque.

    Google Scholar 

  12. W. Paul. "A 2.5 N lower bound for the combinational complexity of Boolean functions", Proc. 7th Ann. ACM Symp. on Th. of Comp. Albuquerque (1975), 27–36.

    Google Scholar 

  13. N. Pippenger. "Short formulae for symmetric functions", IBM Research Report RC-5143, Yorktown Hts., 1974.

    Google Scholar 

  14. N. Pippenger. "Short monotone formulae for threshold functions". IBM Research Report RC 5405, Yorktown Hts., 1975.

    Google Scholar 

  15. V.R. Pratt. "The effect of basis on size of Boolean expressions". Proc. 16th Annual IEEE Symposium on Foundations of Computer Science, 119–121.

    Google Scholar 

  16. J.E. Savage. The Complexity of Computing, Wiley-Interscience, New York, 1976.

    Google Scholar 

  17. C.E. Shannon. "The synthesis of two-terminal switching circuits", Bell System Technical Journal 28 (1949), 59–98.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1977 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Paterson, M.S. (1977). New bounds on formula size. In: Theoretical Computer Science. Lecture Notes in Computer Science, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08138-0_2

Download citation

  • DOI: https://doi.org/10.1007/3-540-08138-0_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08138-8

  • Online ISBN: 978-3-540-37389-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics