Research and Advances

Combining decision rules in a decision table

The techniques for minimizing logic circuits are applied to the simplification of decision tables by the combining of decision rules. This method is logically equivalent to the Quine-McCluskey method for finding prime implicants. If some of the decision rules implied in the ELSE Rule occur with low frequency, then the ELSE Rule can be used to further simplify the decision table. Several objectives merit consideration in optimizing a decision table: reducing machine execution time; reducing preprocessing time; reducing required machine memory; reducing the number of decision rules. (This often improves the clarity of the decision table to a human reader.) It will be shown that objectives (3) and (4) can be furthered with the above methods. Objective (1) is also attained if overspecified decision rules are not combined. Objective (2) must be compared against the potential benefits of objectives (1), (3), and (4) in deciding whether to use the above methods.


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Research and Advances

Extending the infomation theory approach to converting limited-entry decision tables to computer programs

This paper modifies an earlier algorithm for converting decision tables into flowcharts which minimize subsequent execution time when compiled into a computer program. The algorithms considered in this paper perform limited search and, accordingly, do not necessarily result in globally optimal solutions. However, the greater search effort needed to obtain a globally optimal solution for complex decision tables is usually not justified by sufficient savings in execution time. There is an analogy between the problem of converting decision tables into efficient flowcharts and the well-understood problem in information theory of noiseless coding. The results of the noiseless coding literature are used to explore the limitations of algorithms used to solve the decision table problem. The analogy between the two problems is also used to develop improvements to the information algorithm in extending the depth of search under certain conditions and in proposing additional conditions to be added to the decision table. Finally, the information algorithm is compared with an algorithm proposed in a recent paper by Verhelst.
Research and Advances

Conversion of limited-entry decision tables to computer programs—a proposed modification to Pollack’s algorithm

Pollack has proposed an algorithm for converting decision tables into flowcharts which minimize subsequent execution time when compiled into a computer program. Two modifications o this algorithm are proposed. The first relies on Shannon's noiseless coding theorem and the communications concept of entropy but does not completely test the ELSE Rule. The second modification completely tests the ELSE Rule but results in more executions than the first modification. Both modifications result in lower execution time than Pollack's algorithm. However, neither modification guarantees a globally optimal solution.

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