The reachability matrix is a binary DSM with the diagonal elements equal
to "ONE".
The method calls for finding a multi-level hierarchical decomposition
for the matrix. The top level in this hierarchy is composed of all elements
that require no input or are independent from all other elements in the
matrix. Any two elements at the same level of the hierarchy are either
not connected to each other or are part of the same circuit at that level.
Once the top level set of elements is identified, the elements in the top
level set and their corresponding from/to connections are removed from
the matrix leaving us with a sub-matrix that has its own top level set.
The top level set of this sub-matrix will be the second level set of the
original matrix. Proceeding in this manner, all the levels of the matrix
can be identified.
The steps of the method are:
1. Construct a table with four columns.
a. In the first column, list all the elements in the matrix.
b. In the second column, list the set of all the input elements for each row in your table. This set can easily be identified by observing an entry of "ONE" in the corresponding row in the DSM. (Include the element itself as an input).
c. In the third column, list the set of all output elements for each
row in your table. This set can easily be identified by observing an entry of "ONE" in the corresponding column in the DSM. (Include the element itself as an output).
d. In the fourth column, list the intersection of the input and output
sets for each element in your table.
2. Identify top level elements and remove them from the table. An element is in the top level hierarchy of the matrix if its input set is equal to the intersection set.
3. Go to step 1.
Example
An excellent step-by-step example can be found in Warfield (1973).
