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Sums of Read-Once Formulas: How Many Summands Suffice?

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Computer Science – Theory and Applications (CSR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9691))

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Abstract

An arithmetic read-once formula (ROF) is a formula (circuit of fan-out 1) over \(+, \times \) where each variable labels at most one leaf. Every multilinear polynomial can be expressed as the sum of ROFs. In this work, we prove, for certain multilinear polynomials, a tight lower bound on the number of summands in such an expression.

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Notes

  1. 1.

    A polynomial is multilinear if the individual degree of each variable is at most one.

References

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Author information

Authors and Affiliations

  1. The Institute of Mathematical Sciences, Chennai, India

    Meena Mahajan & Anuj Tawari

Authors
  1. Meena Mahajan
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  2. Anuj Tawari
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Correspondence to Anuj Tawari .

Editor information

Editors and Affiliations

  1. Russian Academy of Sciences, St. Petersburg, Russia

    Alexander S. Kulikov

  2. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Gerhard J. Woeginger

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Mahajan, M., Tawari, A. (2016). Sums of Read-Once Formulas: How Many Summands Suffice?. In: Kulikov, A., Woeginger, G. (eds) Computer Science – Theory and Applications. CSR 2016. Lecture Notes in Computer Science(), vol 9691. Springer, Cham. https://doi.org/10.1007/978-3-319-34171-2_19

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  • DOI: https://doi.org/10.1007/978-3-319-34171-2_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-34170-5

  • Online ISBN: 978-3-319-34171-2

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