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A Subquadratic Upper Bound on Sum-Of-Squares Composition Formulas

Author Pavel Hrubeš

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Author Details

Pavel Hrubeš
  • Institute of Mathematics of ASCR, Prague, Czech Republic

Funding

  • Hrubeš, Pavel: This work was supported by Czech Science Foundation GAČR grant 19-27871X.

Cite AsGet BibTex

Pavel Hrubeš. A Subquadratic Upper Bound on Sum-Of-Squares Composition Formulas. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 12:1-12:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CCC.2024.12

Abstract

For every n, we construct a sum-of-squares identity (∑_{i=1}^n x_i²) (∑_{j=1}^n y_j²) = ∑_{k=1}^s f_k², where f_k are bilinear forms with complex coefficients and s = O(n^1.62). Previously, such a construction was known with s = O(n²/log n). The same bound holds over any field of positive characteristic.

Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • Sum-of-squares composition formulas
  • Hurwitz’s problem
  • non-commutative arithmetic circuit

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