A Quadratic Lower Bound for Noncommutative Circuits

Pratik Shastri

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arXiv · 2604.20575

A Quadratic Lower Bound for Noncommutative Circuits

Pratik Shastri

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Abstract

We prove that every fan-in $2$ noncommutative arithmetic circuit computing the palindrome polynomial has size $\Omega(nd)$. In particular, when $d=n$ we obtain an $\Omega(n^2)$ lower bound. The proof builds on and refines a previous work of the author. Key ideas in the proof were generated by Gemini 3.1 Pro.

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Pratik Shastri. 2026-04-22. A Quadratic Lower Bound for Noncommutative Circuits. https://arxiv.org/abs/2604.20575

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