A Framework for the Verification of Certifying Computations

TL;DR

This paper presents a comprehensive framework combining automatic and interactive theorem proving tools to verify certifying computations, enhancing trustworthiness of complex algorithms and their implementations.

Contribution

It introduces a novel framework that integrates VCC and Isabelle/HOL for verifying certifying algorithms, demonstrated on the LEDA library.

Findings

Successful verification of industrial-level algorithms

Effective combination of automatic and interactive verification tools

Enhanced trust in algorithm correctness through certifying checks

Abstract

Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms compute in addition to each output a witness certifying that the output is correct. A checker for such a witness is usually much simpler than the original algorithm - yet it is all the user has to trust. The verification of checkers is feasible with current tools and leads to computations that can be completely trusted. We describe a framework to seamlessly verify certifying computations. We use the automatic verifier VCC for establishing the correctness of the checker and the interactive theorem prover Isabelle/HOL for high-level mathematical properties of algorithms. We demonstrate the effectiveness of our approach by presenting the verification of typical examples of the industrial-level and widespread algorithmic library LEDA.