Search arXivSearch

arXiv · 2505.23311

Towards LLM-based Generation of Human-Readable Proofs in Polynomial Formal Verification

Abstract

Verification is one of the central tasks in circuit and system design. While simulation and emulation are widely used, complete correctness can only be ensured based on formal proof techniques. But these approaches often have very high run time and memory requirements. Recently, Polynomial Formal Verification (PFV) has been introduced showing that for many instances of practical relevance upper bounds on needed resources can be given. But proofs have to be provided that are human-readable. Here, we study how modern approaches from Artificial Intelligence (AI) based on Large Language Models (LLMs) can be used to generate proofs that later on can be validated based on reasoning engines. Examples are given that show how LLMs can interact with proof engines, and directions for future work are outlined.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Rolf Drechsler. 2025-05-29. Towards LLM-based Generation of Human-Readable Proofs in Polynomial Formal Verification. https://arxiv.org/abs/2505.23311

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Deciding Predicate Logical Theories of Real-Valued Functions

The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that reason about real-valued functions. This paper defines a first-order predicate language for reasoning about multi-dimensional smooth real-valued functions and their derivatives, and demonstrates that - despite the obvious undecidability barriers - certain positive decidability results for such a language are indeed possible.

cs.LO

Structural Liveness of Conservative Petri Nets

We show that the EXPSPACE-hardness result for structural liveness of Petri nets [Jancar and Purser, 2019] holds even for a simple subclass of conservative nets. As our main result, we prove that for structurally live conservative nets, the values of the minimal live markings are at most doubly exponential in the size of the net. This implies the EXPSPACE-completeness of structural liveness for conservative Petri nets. The result also applies to structurally bounded Petri nets, whereas the complexity of the general case remains open. As a proof ingredient of independent interest, we present an extension of known results on the bounds of minimal integer solutions to Boolean combinations of linear equalities, inequalities, and divisibility constraints.

cs.LO

Verifying Numerical Methods with Isabelle/HOL

Modern machine learning pipelines and ODE solvers are built on numerical algorithms. Reliable numerical methods are thus a prerequisite for trustworthy machine learning and cyber-physical systems. We evaluate a framework designed for verifying imperative programs and the Isabelle proof assistant as tools for proving the total correctness of four numerical algorithms: the bisection method, the fixed-point method, the perceptron, and the gradient descent algorithm. Our verifications required subtle extensions and generalisations to Isabelle's version of Taylor's theorem and higher-order derivatives. Finally, we reflect on the framework's automation, friendly syntax, and on further requirements to turn it into a verification tool for numerical methods.

cs.LO