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Probably correct row echelon form in the F4 algorithm — arXiv:2609.14433

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.14433
License (as archived): CC0-1.0
Archived: 2026-10-16T02:15:40.585Z
SHA-256 of the archived text: 40ecf9b6257528194442d8d692abdc06298e6d4a7158bbed9fed89e58d628e87
Stable URL of this page: https://metraipolis.com/documento/dc_eb9518ebfd86

How to cite

Probably correct row echelon form in the F4 algorithm — arXiv:2609.14433 — arXiv (en), https://arxiv.org/abs/2609.14433 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_eb9518ebfd86 (Metraipolis archive dc_eb9518ebfd86, sha256 40ecf9b6257528194442d8d692abdc06298e6d4a7158bbed9fed89e58d628e87)

BibTeX

@misc{dceb9518ebfd86,
  title = {Probably correct row echelon form in the F4 algorithm — arXiv:2609.14433},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.14433},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_eb9518ebfd86; sha256 40ecf9b6257528194442d8d692abdc06298e6d4a7158bbed9fed89e58d628e87},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.14433. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The computation of row echelon form is one of the main bottlenecks in the F4 algorithm. Several state of the art implementations use a probabilistic algorithm attributed to Monagan, Pearce, and Steel to accelerate this computation. Despite this, no bound on the probability that the algorithm returns an incorrect result appears to be available. In this paper, we provide such a bound. Furthermore, building on this result, we propose a Las-Vegas variant of the F4 algorithm and show experimentally that it can outperform deterministic F4 on some classical examples.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-15 in cs.DS).
Categorie arXiv: Symbolic Computation (cs.SC) ; Data Structures and Algorithms (cs.DS).
Pagina del lavoro: https://arxiv.org/abs/2609.14433 — 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 2026-10-16T01:54:07.140Z dalla pagina https://arxiv.org/catchup/cs.DS/2026-09-15?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).