Exploiting Positive Equality in a Logic of Equality with Uninterpreted Functions

Abstract. In using the logic of equality with unininterpreted functions to verify hardware systems, specific characteristics of the formula describing the correctness condition can be exploited when deciding its validity. We distinguish a class of terms we call “p-terms” for which equality comparisons can appear 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 considering 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 formula into one in propositional logic by interpreting the formula over a domain of fixed-length bit vectors and using vectors of propositi...

• Type: Conference
• Year: 1999
• Where: CAV
• Authors: Randal E. Bryant, Steven M. German, Miroslav N. Velev
• Keywords: Associated Function Symbols, CAV 1999, Equality Comparisons, Hardware, Propositional Variables