Browse Prior Art Database

# Determining the Logical Sequence in Decision Tables

IP.com Disclosure Number: IPCOM000081377D
Original Publication Date: 1974-May-01
Included in the Prior Art Database: 2005-Feb-27
Document File: 2 page(s) / 14K

IBM

## Related People

Dapron, FE: AUTHOR

## Abstract

When the logic of an algorithm is to be implemented by sequential testing of the logical variables, one of the sequence constraints is: The presence of don't-cares, implied N, implied Y, implied empty-set, discontinuous range, overlapping range, and other logical discontinuities implies a testing sequence which will make them determinate prior to their occurrence.

This text was extracted from a PDF file.
This is the abbreviated version, containing approximately 52% of the total text.

Page 1 of 2

Determining the Logical Sequence in Decision Tables

When the logic of an algorithm is to be implemented by sequential testing of the logical variables, one of the sequence constraints is: The presence of don't- cares, implied N, implied Y, implied empty-set, discontinuous range, overlapping range, and other logical discontinuities implies a testing sequence which will make them determinate prior to their occurrence.

If the logic is represented by a decision table, the test for whether a discontinuity is determinate is that sequentially precedent to it, there must have been some difference between the rule containing the discontinuity and all rules not containing it, and that this difference be some explicit value, i.e., not a don't- care. An extension of the technique set forth in the IBM Technical Disclosure Bulletin Vol. 13, No. 7, (December 1970), page 2034, paragraph 7, will greatly simplify determination of logical sequence constraints, as follows: Preparation of the Table.

While not absolutely necessary, it is very helpful to order the rules by sorting the columns according to some fixed collating sequence, with the top of the column considered the most significant position. The examples presented here will use the collating sequence Y, N, -. The sort will tend to group logical discontinuities justified by a common condition or set of conditions. Isolating the Determining Differences.

For each group of rules containing a discontinuity, the Boolean minimum sum expression is formed by normal Boolean reduction. This minimum sum expression is then compared to a similar minimum sum expression obtained by reducing all rules which did not contain the discontinuity. The differences, more significant than a discontinuity, i.e., in explicit values, between the minimum sum expressions, expressed in terms of the expression from the rules containing the discontinuity, will be the required logical precedent. Validating the Sequence.

If the conditions are posted to a precedence matrix, the viability/ or lack of it, in the sequence will be immediately revealed by the patterns of conditions relative to the principal diagonal. Any condition on the diagonal discloses a singular matrix, i.e., a condition must precede itself. Any conditions to the right of the diagonal discloses a defective sequence. If all conditions are to the left of the diagonal, the sequence is viable. If, in addition, all rows show a condition immediately adjacent to the diagonal, the sequence is the only viable one.

The rules containing C3=- are 3, 4, 7 and 8. The Boolean reduction tree for these rules is 3 YN-Y 4 YN-N 3,4 YN-- 7 NN-Y 3,4,7,8 -N-- 8 NN-N 7,8 NN--.

The rules not containing C3=- are 1, 2, 5 and 6. The Boolean reduction tree for these rules is 1 YYY2...