Holistic Rigorous Numerical Verification

Description du projet

Vérifier la précision des programmes numériques

Une vérification rigoureuse garantit qu’un programme se comporte comme prévu pour toutes les entrées valides. La vérification des programmes numériques qui utilisent des nombres en précision finie est particulièrement difficile en raison des erreurs d’arrondi. Le projet HORNET, financé par le CER, vise à rendre la vérification numérique rigoureuse largement applicable en repensant les techniques de vérification et de débogage automatisées pour les programmes numériques. Il propose une nouvelle approche pour la vérification de l’exactitude basée sur le raisonnement relationnel déductif, qui liera efficacement la différence entre les résultats spécifiés et les résultats calculés du programme. L’approche sera modulaire, automatisée et intégrée à la vérification des propriétés de non-précision, afin d’optimiser les programmes en toute sécurité. HORNET concevra également des techniques complémentaires pour aider les développeurs à déboguer les tentatives de vérification infructueuses.

Objectif

My goal is to make rigorous numerical verification widely applicable and practically usable. Rigorous verification proves at compile-time that a program computes for all valid inputs what it is expected to. It is especially important for numerical programs, which are widely used across application domains and are often safety-critical. However, automated verification of numerical programs over finite-precision (e.g. floating-point) numbers is currently limited. Finite precision introduces rounding errors w.r.t. an ideal, real-valued specification and poses unique challenges for verification of program accuracy and other kinds of desirable properties. As a result, verification of non-trivial numerical programs today requires extensive expert knowledge and mostly manual proofs. Additionally, when verification fails, e.g. because a program is buggy, developers have little debugging help available.

I will rethink automated verification and debugging techniques for numerical programs from the ground up with accuracy as a core property. I propose a novel approach for accuracy verification based on deductive relational reasoning that will be able to effectively bound the difference between the specified (real-valued) and actually computed (finite-precision) program results. My verification approach will be modular, automated, integrate with verification of non-accuracy properties and allow safe program optimizations for real-world programs. To further ensure the practical usability of the verifier, I will develop complementary techniques that will help developers to debug unsuccessful verification attempts, by helping to fix specifications, localize faults in the program and communicate effectively with the verifier.

I will build on my comprehensive expertise with automated rigorous accuracy analysis and optimization of finite-precision arithmetic, and my recent efforts in deductive verification of floating-point runtime errors and numerical specification inference.