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 formalising this idea and, as illustration, construct and analyse straight-line programs for the Bruhat decomposition of $d\times d$ matrices with determinant $1$ over a finite field of order $q$ that have length $O(d^2\log(q))$ and require storing only $O(\log(q))$ matrices during evaluation.

翻译：我们建议，为代数计算设计的直线程序应附带全面的复杂度分析，该分析需同时考虑所需基本代数运算的数量以及求值过程中产生的内存需求。我们引入了一种形式化这一思想的方法，并作为例证，针对有限域F_q上行列式为1的d×d矩阵的Bruhat分解，构造并分析了相应的直线程序。该程序长度为O(d^2 log(q))，且求值过程中仅需存储O(log(q))个矩阵。