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DERIVATION OF THB CHARACfl!RISTIC Loo,c EQUATION
The characteristic logic equation expresses the necessary
and sufficient conditions to be satisfied by the entries in an
interconnection matrix M8,. that interconnects two hierarchical
digraphs A* and B* for which M,18 = 0.
Digraphs A* and B* are described by the reachability
matrices M,1,1a nd M88, respectively. Each of these matrices
can be assumed to have the following properties.
a) The indices of the matrix are ordered in blocks
corresponding to levels in the hierarchical relation, beginning
with the highest level and ending with the lowest.
b) As a consequence of a), every entry to the right of the
main diagonal is 0.
c) By definition, the main diagonal is filled with I's.
d) By definition, the Boolean square of the matrix is
identical to the matrix.
e) Because of d), the matrix is its own transitive
closure [I].
Reachability for the digraph c• that results from the
interconnection is described by the reachability matrix M cc,
which can be assumed to have the following properties.
I) Mee can be written in the form

Characteristic Logic Equations - Revision history

Laouris: Created page with "DERIVATION OF THB CHARACfl!RISTIC Loo,c EQUATION The characteristic logic equation expresses the necessary and sufficient conditions to be satisfied by the entries in an inter..."