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Lower Bounds Beyond DNF of Parities

Authors Artur Riazanov , Anastasia Sofronova , Dmitry Sokolov

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LIPIcs.ITCS.2026.112.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Circuit complexity
Keywords
  • boolean circuits
  • top-down
  • unpredictability

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Abstract

We consider a subclass of AC⁰[2] circuits that simultaneously captures DNF∘Xor and depth-3 AC⁰ circuits. For this class we show a technique for proving lower bounds inspired by the top-down approach. We give lower bounds for the middle slice function, inner product function, and affine dispersers.

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Artur Riazanov, Anastasia Sofronova, and Dmitry Sokolov. Lower Bounds Beyond DNF of Parities. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 112:1-112:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.112

Author Details

Artur Riazanov
  • EPFL, Lausanne, Switzerland
Anastasia Sofronova
  • EPFL, Lausanne, Switzerland
Dmitry Sokolov
  • EPFL, Lausanne, Switzerland
  • Université de Montréal, Canada

Funding

Authors are supported by the Swiss State Secretariat for Education, Research and Innovation (SERI) under contract number MB22.00026.

Acknowledgements

We thank Mika Göös for fruitful discussions. We also thank Pengxiang Wang and anonymous reviewers for useful comments on the text. In particular, we thank a CCC 2025 reviewer who pointed out an issue with the proof of Theorem 16 in the earlier version of the paper.

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