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Berkowitz's Algorithm and Clow Sequences

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Michael Soltys

Rings and Algebras · Submitted 31 Jan 2002

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The main contribution of this paper is a proof of correctness of Berkowitz's algorithm in terms of clow sequences.

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arXiv IDmath/0201315 (version 1)
Pith IDM2HCNUL4, Pith's permanent record of this paper and its review
CitationMichael Soltys. "Berkowitz's Algorithm and Clow Sequences." arXiv:math/0201315 (2002). https://pith.science/paper/M2HCNUL4
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,563 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.41 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; .

We present a combinatorial interpretation of Berkowitz's algorithm. Berkowitz's algorithm is the fastest known parallel algorithm for computing the characteristic polynomial of a matrix. Our combinatorial interpretation is based on ``loop covers'' introduced by Valiant, and ``clow sequences.'' Clow sequences turn out to capture very succinctly the computations performed by Berkowitz's algorithm, which otherwise is quite difficult to analyze. The main contribution of this paper is a proof of correctness of Berkowitz's algorithm in terms of clow sequences.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present a combinatorial interpretation of Berkowitz's algorithm. contribution 1.00 0.93 0.06 asserted 1.00
s1 Berkowitz's algorithm is the fastest known parallel algorithm for computing the characteristic polynomial of a matrix. background 1.00 0.06 0.03 asserted 1.00
s2 Our combinatorial interpretation is based on ``loop covers'' introduced by Valiant, and ``clow sequences.'' Clow sequences turn out to capture very succinctly the computations performed by Berkowitz's algorithm, which otherwise is quite difficult to analyze. method 0.83 0.61 0.07 asserted 1.00
s3 The main contribution of this paper is a proof of correctness of Berkowitz's algorithm in terms of clow sequences. contribution 1.00 0.94 0.92 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We present a combinatorial interpretation of Berkowitz's algorithm. Berkowitz's algorithm is the fastest known parallel algorithm for computing the characteristic polynomial of a matrix. Our combinatorial interpretation is based on ``loop covers'' introduced by Valiant, and ``clow sequences.'' Clow sequences turn out to capture very succinctly the computations performed by Berkowitz's algorithm, which otherwise is quite difficult to analyze. The main contribution of this paper is a proof of correctness of Berkowitz's algorithm in terms of clow sequences.

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