r-map: Relating Implementation and Specification in Hardware Refinement Checking

Refinement checking is an important formal verification method that checks if a hardware implementation complies with (in other words, refines) a given specification. It has been widely used in processor and nonprocessor verification. In refinement checking, a refinement mapping is needed to relate the implementation and the specification. Despite the wide adoption of refinement checking, there is currently no general format or standard for the mapping—most prior works employed a certain property specification language (e.g., the SystemVerilog assertion) to write ad-hoc properties that describe the mapping relation. These manually written properties are usually not well structured and are often difficult to design or understand. In this article, we present
${\tt r{-}map}$
, a language for refinement mapping.
${\tt r{-}map}$
relates the implementation and the specification in a more concise and comprehensible way. We evaluate
${\tt r{-}map}$
in the refinement checking of practical hardware designs. In our case study,
${\tt r{-}map}$
shows a significant reduction of human efforts compared to manually writing refinement properties. We also show how
${\tt r{-}map}$
can help to scale up formal verification.