Boolean Matrix Representation of Graph
A relation R or graph on a finite set can be expressed as a boolean matrix M where:
M[i, j] = 1 iff (i, j) &isin R .
Multiplication of boolean matrices is done in the same way as ordinary matrix multiplication, but using &and for · and &or for + .
|Identity, R0||In (identity matrix)|
|Inverse, R-1 or &Gamma-1||MT|
|Reflexive||I &sube M|
|Symmetric||M = MT|
|Transitive||M2 &sube M|
|Antisymmetric||M &cap MT &sube In|
|Paths of length n||Mn|
|Transitive closure &Gamma+||&cupi=1n Mi|
|Reflexive transitive closure &Gamma*||&cupi=0n Mi|
Example: Let the set S be basic blocks of a program and &Gamma be transfers of control between blocks.
Contents    Page-10    Prev    Next    Page+10    Index