A THEOREM ON BOOLEAN MATRICES
A THEOREM ON BOOLEAN MATRICES
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DOI：
10.1145/321105.321107
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发表时间：
1962-01-01
影响因子：
2.5
通讯作者：
WARSHALL, S
中科院分区：
文献类型：
--
作者：
WARSHALL, S
用布尔矩阵表示程序拓扑（Presser [1]，Marimont [2]，t 'or example）引起了人们对将d× d布尔矩阵M变换为d× d布尔矩阵M'的算法的兴趣，M '= v M s其中定义M ~= MandM~+ I= M~ AM。4= 1将变换描述为布尔乘积的布尔和的方便性显然已经提出了相应的算法，其运行时间随着d的立方而增加--其他条件相同。虽然避免评论这种矩阵的效用的区域，我们证明了算法的有效性，其运行时间上升略快于d的平方。
The use of boolean matrices to represent program topology (Presser [1], and Marimont [2], t'or example) has led to interest in algorithms for transforming the d× d boolean matrix M to the d× d boolean matrix M'given by: d M'= v M s where we defineM~= MandM~+ I= M~ AM. 4= 1 ne convenience of describing the transformation as a boolean sum of boolean products has apparently l suggested the corresponding algorithms, the running times of which increase--other things being equal--as the cube of d. While refraining from comment on the area of utility of such matrices, we prove the validity of an algorithm whose running time goes up slightly faster than the square of d.