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Conference on Computability in Europe

CiE 2010: Programs, Proofs, Processes pp 239–245Cite as

Circuit Complexity and Multiplicative Complexity of Boolean Functions

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6158))

Abstract

In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3 − c lower bound on the circuit complexity of a large class of functions representable by high degree polynomials over GF(2). The key idea of the proof is a circuit complexity measure assigning different weights to XOR and AND gates.

Research is partially supported by Federal Target Programme “Scientific and scientific-pedagogical personnel of the innovative Russia” 2009–2013, RFBR (08-01-00640 and 09-01-12137), RAS Program for Fundamental Research, Grant of the President of Russian Federation (MK-3912.2009.1 and NSh-5282.2010.1), and ANR, France (NAFIT ANR-08-EMER-008-01).

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References

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Author information

Authors and Affiliations

  1. St. Petersburg Department of Steklov Institute of Mathematics,  

    Arist Kojevnikov & Alexander S. Kulikov

Authors
  1. Arist Kojevnikov
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  2. Alexander S. Kulikov
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Editor information

Editors and Affiliations

  1. Departamento de Matemática, Universidade de Lisboa, Campo Grande, Edifício C6, 1749-016, Lisboa, Portugal

    Fernando Ferreira

  2. Institute for Logic, Language and Computation (ILLC), Universiteit van Amsterdam, P.O. Box 94242, 1090, Amsterdam, GE, The Netherlands

    Benedikt Löwe

  3. Departamento de Informática e Ingeniería de Sistemas, Universidad de Zaragoza, María de Luna 1, 50018, Zaragoza, Spain

    Elvira Mayordomo

  4. Universidade dos Açores, Campus de Ponta Delgada, Apartado 1422, 9501-801, Ponta Delgada, Açores, Portugal

    Luís Mendes Gomes

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Kojevnikov, A., Kulikov, A.S. (2010). Circuit Complexity and Multiplicative Complexity of Boolean Functions . In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_27

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  • DOI: https://doi.org/10.1007/978-3-642-13962-8_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13961-1

  • Online ISBN: 978-3-642-13962-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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