2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63245We 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.Submitted to ELA (Electronic Journal of Linear Algebra)Rings and Algebras65F30; 11Y16text