The Vertex-Frame Method for Obtaining Minimal Proposition-Letter Formulas

Abstract

The vertex frame is similar to an n-dimensional cube or Tychonoff frame that has been cut and unfolded into the shape of a Karnaugh map. The methods of use are similar to those for Karnaugh maps. Minimal disjunctive and conjunctive normal formulas are found for problems with or without don't-care cases. The selection graph, a linear graph, is used to enhance the prime antecedent (= prime implicant) selection procedure. The vertex frame readily handles most problems of up to six variables. Problems with seven and eight variables have been worked successfully, but this is an area where more experience is needed in working out actual problems that arise in engineering practice. As with any map method, pattern recognition plays an important role, and thus it takes longer to become proficient in this method than in some of the formula-manipulation methods (e.g., Quine's, McCluskey's, Mott's). The problem of recognizing plots, on a vertex frame, of symmetric and unate truth functions is discussed.