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A system of conservative transformation rules is presented for abstracting memories whose forwarding logic interacts with stalling conditions for preserving the memory semantics in microprocessors with in-order execution. Microprocessor correctness is expressed in the logic of Equality with Uninterpreted Functions and Memories (EUFM) [6]. Memory reads and writes are abstracted as arbitrary uninterpreted functions in such a way that the forwarding property of the memory semantics-- that a read returns the data most recently written to an equal write address--is satisfied completely only when exactly the same pair of one read and one write address is compared for equality in the stalling logic. These transformations are applied entirely automatically by a tool for formal verification of microprocessors, based on EUFM, the Burch and Dill flushing technique [6], and the properties of Positive Equality [3]. An order of magnitude reduction is achieved in the number of eij Boolean variables [9] that encode the equality comparisons of register identifiers in the correctness formulas for single-issue pipelined and dual-issue superscalar microprocessors with multicycle functional units, exceptions, and branch prediction. That results in up to 40脳 reduction in the CPU time for the formal verification of the dual-issue superscalar microprocessors.

Automatic Abstraction of Memories in the Formal Verification of Superscalar Microprocessors