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New Lower Bounds Against Homogeneous Non-Commutative Circuits

Authors Prerona Chatterjee , Pavel Hrubeš

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Author Details

Prerona Chatterjee
  • Department of Computer Science, Tel Aviv University, Israel
Pavel Hrubeš
  • Institute of Mathematics, Czech Academy of Sciences, Prague, Czech Republic

Funding

  • Chatterjee, Prerona: Funded by the Azrieli International Fellowship. This work was done while the author was a postdoctoral researcher at the Czech Academy of Sciences, Prague, and was funded by Czech Science Foundation GAČR grant 19-27871X.
  • Hrubeš, Pavel: Czech Science Foundation GAČR grant 19-27871X.

Acknowledgements

Prerona would like to acknowledge https://www.cafedu.cz/en/ for being such a nice place to work from. Pavel thanks Amir Yehudayoff for useful ideas on this topic which were exchanged in distant and joyous past.

Cite AsGet BibTex

Prerona Chatterjee and Pavel Hrubeš. New Lower Bounds Against Homogeneous Non-Commutative Circuits. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 13:1-13:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.CCC.2023.13

Abstract

We give several new lower bounds on size of homogeneous non-commutative circuits. We present an explicit homogeneous bivariate polynomial of degree d which requires homogeneous non-commutative circuit of size Ω(d/log d). For an n-variate polynomial with n > 1, the result can be improved to Ω(nd), if d ≤ n, or Ω(nd (log n)/(log d)), if d ≥ n. Under the same assumptions, we also give a quadratic lower bound for the ordered version of the central symmetric polynomial.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algebraic complexity theory
Keywords
  • Algebraic circuit complexity
  • Non-Commutative Circuits
  • Homogeneous Computation
  • Lower bounds against algebraic circuits

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