Topology inside NC$^1$

Eric Allender; Samir Datta; Arsenii Karnaukhov; Sambuddha Roy; Alexander Shekhovstov

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arXiv · 2609.11822

Topology inside NC$^1$

Eric Allender·Samir Datta·Arsenii Karnaukhov·Sambuddha Roy·Alexander Shekhovstov

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Abstract

We show that ACC$^0$ is precisely what can be computed with constant-width circuits of polynomial size and polylogarithmic genus. This extends a characterization given by Hansen, showing that planar constant-width circuits also characterize ACC$^0$. Thus polylogarithmic genus provides no additional computational power in this model. We consider other generalizations of planarity, including crossing number and thickness. We show that constant-width circuits of polynomial size and thickness two already suffice to capture all of NC$^1$.

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BibTeX RIS

Eric Allender, Samir Datta, Arsenii Karnaukhov, Sambuddha Roy, Alexander Shekhovstov. 2026-09-10. Topology inside NC$^1$. https://arxiv.org/abs/2609.11822

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