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Lower Bounds for Unrestricted Boolean Circuits: Open Problems

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Computer Science – Theory and Applications (CSR 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10846))

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Abstract

To prove that \(\text {P} \ne \text {NP}\), it suffices to prove a superpolynomial lower bound on Boolean circuit complexity of a function from NP. Currently, we are not even close to achieving this goal: we do not know how to prove a 4n lower bound. What is more depressing is that there are almost no techniques for proving circuit lower bounds.

In this note, we briefly review various approaches that could potentially lead to stronger linear or superlinear lower bounds for unrestricted Boolean circuits (i.e., circuits with no restriction on depth, fan-out, or basis).

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Acknowledgments

The research is supported by Russian Science Foundation (project 16-11-10123). The author is thankful to Alexander Golovnev and Edward A. Hirsch for fruitful discussions and many useful comments.

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Authors and Affiliations

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

    Alexander S. Kulikov

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  1. Alexander S. Kulikov
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Correspondence to Alexander S. Kulikov .

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Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Fedor V. Fomin

  2. Steklov Mathematical Institute, Moscow, Russia

    Vladimir V. Podolskii

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Kulikov, A.S. (2018). Lower Bounds for Unrestricted Boolean Circuits: Open Problems. In: Fomin, F., Podolskii, V. (eds) Computer Science – Theory and Applications. CSR 2018. Lecture Notes in Computer Science(), vol 10846. Springer, Cham. https://doi.org/10.1007/978-3-319-90530-3_2

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  • DOI: https://doi.org/10.1007/978-3-319-90530-3_2

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