Formalizing Pfaffian in bounded arithmetic

Published 2 Apr 2024 in math.LO | (2404.01728v3)

Abstract: We formalize algorithms computing Pfaffian in the theory of bounded arithmetic for sharpL which is based on Berkowitz algorithm for the determinant. We also prove relations among Pfaffian properties. Furthermore, we give an algorithm for Pfaffian pairs as well.

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References (2)

S.J.Berkowitz, On computing the determinant in small parallel time using a small number of processors. Information Processing Letters. 18 (3): pp.147–150 (1984)
M. Mahajan, P. R. Subramanya and V. Vinay, “The Combinatorial Approach Yields an NC Algorithm for Computing Pfaffians”, Discrete Appl. Math., 143:1–3 (2004) 1–16.

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Authors (1)

Satoru Kuroda

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