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Algebraic Characterizations of Small Classes of Boolean Functions

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STACS 2003 (STACS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2607))

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Abstract

Programs over semigroups are a well-studied model of computation for boolean functions. It has been used successfully to characterize, in algebraic terms, classes of problems that can, or cannot, be solved within certain resources. The interest of the approach is that the algebraic complexity of the semigroups required to capture a class should be a good indication of its expressive (or computing) power. In this paper we derive algebraic characterizations for some “small” classes of boolean functions, all of which have depth-3 AC0 circuits, namely k-term DNF, k-DNF, k-decision lists, decision trees of bounded rank, and DNF. The interest of such classes, and the reason for this investigation, is that they have been intensely studied in computational learning theory.

Partially supported by the IST Programme of the EU under contract number IST-1999-14186 (ALCOM-FT), by the Spanish Government TIC2001-1577-C03-02 (LOGFAC), by CIRIT 1997SGR-00366, and TIC2000-1970-CE.

Supported by NSERC, FCAR, and the von Humboldt Foundation.

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Author information

Authors and Affiliations

  1. Department of Software (LSI), Universitat Politècnica de Catalunya, Jordi Girona Salgado 1-3, E-08034, Barcelona, Spain

    Ricard Gavaldà

  2. School of Computer Science, McGill University, 3480 University, H3A 2A7, Québec, Montréal, Canada

    Denis Thérien

Authors
  1. Ricard Gavaldà
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  2. Denis Thérien
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takusstr. 9, 14195, Berlin, Germany

    Helmut Alt

  2. LIRMM, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Michel Habib

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Gavaldà, R., Thérien, D. (2003). Algebraic Characterizations of Small Classes of Boolean Functions. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_30

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  • DOI: https://doi.org/10.1007/3-540-36494-3_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00623-7

  • Online ISBN: 978-3-540-36494-8

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