Skip to main content
SpringerLink
Log in
Book cover

Latin American Symposium on Theoretical Informatics

LATIN 1995: LATIN '95: Theoretical Informatics pp 60–71Cite as

Lower bounds for modular counting by circuits with modular gates

  • Conference paper
  • First Online:

  • 158 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 911))

Abstract

We prove that constant depth circuits, with one layer of MOD m gates at the inputs, followed by a fixed number of layers of MOD p gates, where p is prime, require exponential size to compute the MOD q function, if q is a prime that divides neither p nor q.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

References

  1. M. Ajtai, “Σ 11 formulae on finite structures”, Annals of Pure and Applied Logic 24 (1983) 1–48.

    Article  Google Scholar 

  2. D. Mix Barrington, H. Straubing, and D. Thérien, “Nonuniform Automata over Groups”, Information and Computation 89 (1990) 109–132.

    Article  Google Scholar 

  3. J. Bruck, “Harmonic Analysis of Polynomial Threshold Functions”, SIAM Journal of Discrete Mathematics 3 (1990) 168–177.

    Article  Google Scholar 

  4. M. Furst, J. Saxe, and M. Sipser, “Parity, Circuits, and the Polynomial Time Hierarchy”, J. Math Systems Theory 17 (1984) 13–27.

    Article  Google Scholar 

  5. M. Krause and P. Pudlák, “On the Computational Power of Depth 2 Circuits with Threshold and Modulo Gates”, Proc. 26th ACM STOC (1994) 48–57.

    Google Scholar 

  6. P. McKenzie, P. Péladeau, and D. Thérien, NC 1: “The Automata-Theoretic Approach”, to appear in Theoretical Computer Science.

    Google Scholar 

  7. R. Smolensky, “Algebraic Methods in the Theory of Lower Bounds for Boolean Circuit Complexity”, Proc. 19th ACM STOC (1987) 77–82.

    Google Scholar 

  8. H. Straubing, “Constant-depth Periodic Circuits”, International J. Algebra and Computation 1 (1991) 49–88.

    Article  Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. COINS Department, University of Massachusetts, 01003, Amherst, Massachusetts, USA

    David Mix Barrington

  2. Computer Science Department, Boston College, 02167, Chestnut Hill, Massachusetts, USA

    Howard Straubing

Authors
  1. David Mix Barrington
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Howard Straubing
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ricardo Baeza-Yates Eric Goles Patricio V. Poblete

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Barrington, D.M., Straubing, H. (1995). Lower bounds for modular counting by circuits with modular gates. In: Baeza-Yates, R., Goles, E., Poblete, P.V. (eds) LATIN '95: Theoretical Informatics. LATIN 1995. Lecture Notes in Computer Science, vol 911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59175-3_81

Download citation

  • DOI: https://doi.org/10.1007/3-540-59175-3_81

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59175-7

  • Online ISBN: 978-3-540-49220-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation