Minimal program covering based on the output variables

Abstract

This paper discusses how a program can be represented by a binary relation, R, and how to decompose the latter into a set of rectangular relations. Next, we present our methodology based on relational operators and dependence relations, to show how we can use these rectangles to obtain more interesting ones that describe the entire behavior of every variable in the program. The notion of lattice of maximal rectangles is effective in that it permits to have a particular representation of the program which shows all the different parts that constitute the original program. By looking at this lattice structure, we find that the set of the leaves of this lattice, which represent "pertinent" rectangles associated to output variables, gives a minimal program covering.