An algebraic approach to test data generation
A. Brown · 1972
In this paper the Test Data Generation problem is considered from the point of view of symbolic logic i.e., Boolean algebra. Essentially, the problem is the determination of various transfer functions describing the behavior of the network under test. This can be done by solving a corresponding system of Boolean equations using straight forward and easily understood algebriac techniques.This algebraic approach is enhanced significantly by the use of the novel concepts of logic flowgraphs and variational derivatives. Logic flowgraphs are a particular application of flowgraphs extending to logic networks the signal flow theory and other graphical concepts which have been successfully applied elsewhere. The logic flowgraph results in a visualization and a mechanization of the algebraic approach not evident from other approaches. Indeed it provides a schedule (an ordering relative to precedence) for the above mentioned substitional process.The variational derivative concept, characterizing transitions in a network, is ultimately related to fault detection and is, in effect, an algebraic generalization of the star-product and d-cube concepts of Roth. In fact, the concept provides a concise algebraic means of describing the responses (R (Lt ; Lt-1 )) and (R' (Lt ; Lt-1 ;X)) mentioned above by Mr. Krosner.We will demonstrate the usefulness of these concepts by the analysis of the illustrative examples in figures (1), (2), and (3). Experience has shown that they provide a very general framework from which the broad spectrum of more practical and specialized techniques can be more readily understood.A more extensive and detailed account of the concepts and techniques briefly mentioned here can be found in Reference 1.