Programming Languages: Boolean matrix methods for the detection of simple precedence grammars

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Abstract
The use of decision tables as a tool in systems analysis and for program specification is now becoming accepted. Rules on redundancy, contradiction, and completeness for limited entry tables were published in 1963. These are usually used for checking, preceded if necessary by a conversion from extended to limited entry form. Processors which automatically translate tables to more conventional program usually base their diagnostic facilities on these rules. In this paper it is suggested that these rules are unsatisfactory and that the important aspect of checking is to eliminate ambiguity from tables. Ambiguity is defined and discussed, and a procedure for producing checked-out decision tables is proposed. The theoretical basis of the algorithm used is established. The importance of well-designed diagnostic facilities in decision table processors is emphasized.

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