SMT-Based Theorem Verification for Testing-Based Formal Verification

Abstract

Testing-based formal verification with symbolic execution (TBFV-SE) checks whether programs correctly implement their formal specification. Given a formal specification and a program, it first derives a theorem expressing the correctness property of the executed program paths and then formally verifies the validity of the theorem. However, such theorems still need to be verified manually due to the lack of a tool support for dealing with expressions involved. In this paper, we propose a method for automatically verifying theorems for TBFV-SE. This method uses an SMT solver to check whether a theorem is valid. For this purpose, the method converts the conditions in the theorems written in the SOFL specification language into appropriate constraints that are supported by the SMT solver. We present a tool to support the method, and present two case studies to demonstrate how the tool works in the context of Java programs and SOFL specifications.