A Quadratic Lower Bound for Noncommutative Circuits
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911695659597824 |
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| author | Shastri, Pratik |
| author_facet | Shastri, Pratik |
| contents | 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 $Ω(n^2)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20575 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Quadratic Lower Bound for Noncommutative Circuits Shastri, Pratik Computational Complexity 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 $Ω(n^2)$ 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. |
| title | A Quadratic Lower Bound for Noncommutative Circuits |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2604.20575 |