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


Prerona would like to acknowledge 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.

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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)


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
  • Algebraic circuit complexity
  • Non-Commutative Circuits
  • Homogeneous Computation
  • Lower bounds against algebraic circuits


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