CF-GKAT: Efficient Validation of Control-Flow Transformations

TL;DR

CF-GKAT extends GKAT to handle non-local control flow and concrete values, enabling efficient verification of complex program transformations like goto-elimination and decompilation.

Contribution

It introduces CF-GKAT, a novel system that soundly and completely verifies trace equivalence for programs with non-local control flow, maintaining GKAT's efficiency.

Findings

Successfully verified complex control-flow transformations.

Validated decompiler output and goto-elimination procedures.

Preserved nearly-linear efficiency in extended verification.

Abstract

Guarded Kleene Algebra with Tests (GKAT) provides a sound and complete framework to reason about trace equivalence between simple imperative programs. However, there are still several notable limitations. First, GKAT is completely agnostic with respect to the meaning of primitives, to keep equivalence decidable. Second, GKAT excludes non-local control flow such as goto, break, and return. To overcome these limitations, we introduce Control-Flow GKAT (CF-GKAT), a system that allows reasoning about programs that include non-local control flow as well as hardcoded values. CF-GKAT is able to soundly and completely verify trace equivalence of a larger class of programs, while preserving the nearly-linear efficiency of GKAT. This makes CF-GKAT suitable for the verification of control-flow manipulating procedures, such as decompilation and goto-elimination. To demonstrate CF-GKAT's abilities, we validated the output of several highly non-trivial program transformations, such as Erosa and Hendren's goto-elimination procedure and the output of Ghidra decompiler. CF-GKAT opens up the application of Kleene Algebra to a wider set of challenges, and provides an important verification tool that can be applied to the field of decompilation and control-flow transformation.