Showcasing straight-line programs with memory via matrix Bruhat decomposition

被引：0

作者：

Niemeyer, Alice C. ^{[1
]}

Popiel, Tomasz ^{[2
]}

Praeger, Cheryl E. ^{[3
]}

Rademacher, Daniel ^{[1
]}

机构：

[1] Rhein Westfal TH Aachen, Chair Algebra & Representat Theory, Pontdriesch 10-16, D-52062 Aachen, Germany

[2] Monash Univ, Sch Math, 9 Rainforest Walk, Clayton, Vic 3800, Australia

[3] Univ Western Australia, Ctr Math Symmetry & Computat, 35 Stirling Highway, Crawley, WA 6009, Australia

来源：

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2024年 / 34卷 / 07期

基金：

澳大利亚研究理事会;

关键词：

Straight-Line program; Complexity of algorithms; Bruhat decomposition; memory complexity;

D O I：

10.1142/S0218196724500413

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We suggest that straight-line programs designed for algebraic computations should be accompanied by a comprehensive complexity analysis that takes into account both the number of fundamental algebraic operations needed, as well as memory requirements arising during evaluation. We introduce an approach for formalizing this idea and, as illustration, construct and analyze straight-line programs for the Bruhat decomposition of d x d matrices with determinant 1 over a finite field of order q that have length O(d2log(q)) and require storing only O(log(q)) matrices during evaluation.

引用

页码：1059 / 1090

页数：32

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