A Quadratic Lower Bound for Noncommutative Circuits
Abstract
We prove that every fan-in 2 noncommutative arithmetic circuit computing the palindrome polynomial has size Ω(nd). In particular, when d=n we obtain an Ω(n2) 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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