A Qualitative Reasoning Model for Software Testing, based on Combinatorial Geometry

Abstract

Let us first give a short summary of the paper. We introduce an operational qualitative model for numerical algorithms. This model enables qualitative algorithmic reasoning during the unit testing process, supported by an automatic generation of boundary test data. It contains the spatial encoding of all the functionally equivalent regions (called homodromies). The model, viewed as a qualitative abstraction of the algorithm, is automatically generated thanks to multiple targeted executions of its instrumented basic conditions, that permit the interpolation of a set of linear equations and their corresponding hyperplanes. All feasible paths (when all basic conditions are linear) are identified in the form a Ternary Decision Tree. Each feasible execution path corresponds to a geometric region supported and/or delimited by a finite set of hyperplanes of the vector space. Oriented Matroids allow the encoding of the relative positions of all such regions of various dimensions, in a purely combinatorial way, using a finite signed set system, supported by a rich mathematical theory. This model uses a qualitative space algebra and enables qualitative reasoning: regions are identified according to qualitatively valued inputs, which are, in their turn, propagated through them. The proposed model permits a global/local envisionment 331