On the conversion of decision tables to computer programs

Abstract

The use of execution time diagnostics in pinpointing ambiguities in decision tables is discussed. It is pointed out that any attempt at resolving ambiguities at compile time will, in general, be impossible. It is shown that, as a consequence, tree methods of converting decision tables to programs are inadequate in regard to ambiguity detection. Two algorithms for programming decision tables whose merits are simplicity of implementation and detection of ambiguities at execution time are presented. The first algorithm is for limited entry decision tables and clarifies the importance of proper coding of the information in the decision table. The second algorithm programs a mixed entry decision table directly without going through the intermediate step of conversion to a limited entry form, thereby resulting in storage economy. A comparison of the algorithms and others proposed in the literature is made. Some features of a decision table to FORTRAN IV translator for the IBM 7044 developed by the authors are given.KEY WORDS AND PHRASES: decision tobies, diagnostic aids, system analysis, business applications

Consistance, complétude et traduction optimale des tables de décision

“…Soit S o l'ensemble des 3" a-cubes (a = 0, 1, ...,*) définis sur un «-cube, chaque élément de éf Q est un vecteur noté W k = (e ki , ... 9 e kj9 . ..,e fcn ); e kj e { 0, 1, <p }.…”

“…Mais ils sont très coûteux relativement au critère 3 : la recherche d'une solution optimale est un problème NP-complet, (i. e. que le temps de calcul nécessaire pour faire cette recherche est une fonction exponentielle de la dimension de la table). Les algorithmes dits heuristiques, qui recherchent une solution sous-optimale [2,3,9,10,12,15,17,18], plus performants relativement à ce critère 3, présentent néanmoins un inconvénient majeur : il n'est pas possible de situer, autrement que statistiquement, une solution sous-optimale par rapport à l'optimum, on ne peut même pas majorer l'écart entre les deux.…”

Information theory applied to the conversion of decision tables to computer programs

“…However, if only binary branching is permitted, it would be necessary to convert an extended entry table (explicitly or implicitly) before this algorithm could be applied. On the other hand, it is felt that for direct conversion of extended entry tables to computer programs, mask methods [12] may be preferable.…”

Conversion of decision tables by rule mask method without rule mask

“…Two classes of algorithms exist for the conversion of decision tables to computer programs: tree methods [1][2][3] and mask methods [4][5][6]. For the selection of a method there are two main considerations: (1) the effieiency of the generated program in terms of storage and execution time, and (2) the handling of ambiguities which are an inherent difficulty of decision tables.…”

“…Rule mask methods store the decision table in a (usually) binary mask and interpret this mask at execution time. A very elegant algorithm for this method is shown in [6]. In a resulting vector, say R, ail rules which hold are designated by a 1; all others a 0 ( Figure 4).…”