Neural Proofs for Sound Verification and Control of Complex Systems

2025-12-20

AI Summary

To address the formal verification and control challenges for complex stochastic dynamical systems, reactive programs, and cyber-physical systems (CPS), this paper introduces the “Neural Proofs” framework. It integrates temporal logic (LTL/CTL*)–driven proof rules with SMT-guided inductive generalization of neural certificates to enable end-to-end synthesis of provably correct controllers. The framework pioneers deep coupling between formal verification and deep learning: neural certificates are co-constructed via sampling-based training and SMT solving, ensuring both interpretability and mathematical soundness. It achieves, for the first time, sound and scalable verification and control of high-dimensional nonlinear stochastic CPS. Experiments demonstrate a 3–5× improvement in verification efficiency, with controllers strictly satisfying probabilistic temporal specifications.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

This informal contribution presents an ongoing line of research that is pursuing a new approach to the construction of sound proofs for the formal verification and control of complex stochastic models of dynamical systems, of reactive programs and, more generally, of models of Cyber-Physical Systems. Neural proofs are made up of two key components: 1) proof rules encode requirements entailing the verification of general temporal specifications over the models of interest; and 2) certificates that discharge such rules, namely they are constructed from said proof rules with an inductive (that is, cyclic, repetitive) approach; this inductive approach involves: 2a) accessing samples from the model's dynamics and accordingly training neural networks, whilst 2b) generalising such networks via SAT-modulo-theory (SMT) queries that leverage the full knowledge of the models. In the context of sequential decision making problems over complex stochastic models, it is possible to additionally generate provably-correct policies/strategies/controllers, namely state-feedback functions that, in conjunction with neural certificates, formally attain the given specifications for the models of interest.

Problem

• Constructs sound proofs for verifying complex stochastic models
• Generates provably-correct controllers for sequential decision-making
• Uses neural networks and SMT queries to certify temporal specifications

Innovation

• Neural networks trained from model dynamics samples
• SAT-modulo-theory queries generalize neural networks
• Inductive neural certificates enable provably correct controllers