Timed Refinement for Verification of Real-Time Object Code Programs

Abstract

We introduce a refinement-based notion of correctness for verification of interrupt driven real-time object code programs, called timed refinement. The notion of timed refinement is targeted at verification of low-level object code against high-level specification models. For timed refinement, both the object code (implementation) and the specification are encoded as timed transition systems. Hence, timed refinement can be construed as a notion of equivalence between two timed transition systems that allows for stuttering between the implementation and specification, and also allows for the use of refinement maps. Stuttering is the phenomenon where multiple but finite transitions of the implementation can match a single transition of the specification. Refinement maps allow low-level implementations to be verified against high-level specification models. We also present a procedure for checking timed refinement. The proposed techniques are demonstrated with the verification of object code programs of six case studies from electric motor control applications.