Exploiting Positive Equality in a Logic of Equality with Uninterpreted Functions

In using the logic of equality with unininterpreted functions to ver-ify hardware systems, specific characteristics of the formula describing the cor-rectness condition can be exploited when deciding its validity. We distinguish a class of terms we call “p-terms” for which equality comparisons can appear only in monotonically positive formulas. By applying suitable abstractions to the hardware model, we can express the functionality of data values and instruction addresses flowing through an instruction pipeline with p-terms. A decision procedure can exploit the restricted uses of p-terms by consider-ing only “maximally diverse ” interpretations of the associated function symbols, where every function application yields a different value except when constrained by functional consistency. We present a procedure that translates the original for-mula into one in propositional logic by interpreting the formula over a domain of fixed-length bit vectors and using vectors of propositional variables to encode domain variables. By exploiting maximal diversity, this procedure can greatly reduce the number of propositional variables that must be introduced