# Relational Verification via Invariant-Guided Synchronization

## TL;DR

This paper introduces PEQUOD, a novel verification tool that simultaneously searches for synchronization points and synthesizes relational invariants, enabling the verification of complex relational properties in JVM bytecode that previous methods cannot handle.

## Contribution

It proposes a new approach that integrates invariant synthesis with synchronization point search, improving the verification of relational properties over multiple program executions.

## Key findings

- PEQUOD successfully verifies properties of JVM bytecode that existing tools cannot handle.
- The approach effectively guides synchronization point selection using synthesized invariants.
- PEQUOD outperforms current techniques on challenging verification problems.

## Abstract

Relational properties describe relationships that hold over multiple executions of one or more programs, such as functional equivalence. Conventional approaches for automatically verifying such properties typically rely on syntax-based, heuristic strategies for finding synchronization points among the input programs. These synchronization points are then annotated with appropriate relational invariants to complete the proof. However, when suboptimal synchronization points are chosen the required invariants can be complicated or even inexpressible in the target theory. In this work, we propose a novel approach to verifying relational properties. This approach searches for synchronization points and synthesizes relational invariants simultaneously. Specifically, the approach uses synthesized invariants as a guide for finding proper synchronization points that lead to a complete proof. We implemented our approach as a tool named PEQUOD, which targets Java Virtual Machine (JVM) bytecode. We evaluated PEQUOD by using it to solve verification challenges drawn from the from the research literature and by verifying properties of student-submitted solutions to online challenge problems. The results show that PEQUOD solve verification problems that cannot be addressed by current techniques.