Metraipolis › archive › dc_d60ef2a5ea0d

Topology inside NC$^1$ — arXiv:2609.11822

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.11822
License (as archived): CC0-1.0
Archived: 2026-10-16T06:39:42.643Z
SHA-256 of the archived text: 130fbef824d7caa68846ccd3f18e0e26f32f1f750576ecfe5b9b101ab921b0da
Stable URL of this page: https://metraipolis.com/documento/dc_d60ef2a5ea0d

How to cite

Topology inside NC$^1$ — arXiv:2609.11822 — arXiv (en), https://arxiv.org/abs/2609.11822 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_d60ef2a5ea0d (Metraipolis archive dc_d60ef2a5ea0d, sha256 130fbef824d7caa68846ccd3f18e0e26f32f1f750576ecfe5b9b101ab921b0da)

BibTeX

@misc{dcd60ef2a5ea0d,
  title = {Topology inside NC$^1$ — arXiv:2609.11822},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.11822},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_d60ef2a5ea0d; sha256 130fbef824d7caa68846ccd3f18e0e26f32f1f750576ecfe5b9b101ab921b0da},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.11822. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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$^1$.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-11 in cs.CC).
Categorie arXiv: Computational Complexity (cs.CC).
Pagina del lavoro: https://arxiv.org/abs/2609.11822 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T06:19:27.875Z dalla pagina https://arxiv.org/catchup/cs.CC/2026-09-11?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).