Invariant Synthesis for Incomplete Verification Engines

TL;DR

This paper introduces a framework for synthesizing inductive invariants in incomplete verification engines, enabling sound reduction of complex logical problems to decidable theories through non-provability information and CEGIS-based algorithms.

Contribution

It presents a novel invariant synthesis framework that leverages non-provability information and CEGIS for incomplete verification engines, applicable to undecidable theories.

Findings

Effective invariant synthesis in undecidable theories

Successful handling of quantified formulas and heap properties

Strong results across diverse program verification scenarios

Abstract

We propose a framework for synthesizing inductive invariants for incomplete verification engines, which soundly reduce logical problems in undecidable theories to decidable theories. Our framework is based on the counter-example guided inductive synthesis principle (CEGIS) and allows verification engines to communicate non-provability information to guide invariant synthesis. We show precisely how the verification engine can compute such non-provability information and how to build effective learning algorithms when invariants are expressed as Boolean combinations of a fixed set of predicates. Moreover, we evaluate our framework in two verification settings, one in which verification engines need to handle quantified formulas and one in which verification engines have to reason about heap properties expressed in an expressive but undecidable separation logic. Our experiments show that our invariant synthesis framework based on non-provability information can both effectively synthesize inductive invariants and adequately strengthen contracts across a large suite of programs.