Transitive bordering

Transitive Bordering is a special case of transitive coupling in which the subsystem B consists of a single element.

Transitive Bordering is used for adding a new element to an already existing binary matrix model.

Transitive Bordering can also be employed iteratively in the ISM process for developing the complete binary matrix as soon a portion of the matrix, representing a subset of the set of elements, is filled.

Techniques

• A method that requires the derivation and solution of a set of characteristic logic equations. Warfield [5, Ch. 7]. This approach uses the same principle on which the cascading technique for transi- tive coupling [4] is based.
• In [1] and [2], Warfield has presented a second technique involving the implication matrix.
• A procedure based on the following Theorem

To satisfy the constraints A² + XY = A YX + B² = B

the following must hold for all a k:

1. if a_lk = 0, then X_ltY_tk = 0 for all t, and
2. ifb_lk = 0,then Y_ltX_tk = 0 for aall t.