Related papers: ML4PG in Computer Algebra verification

When improving results about generalized inverses, the aim often is to do this in the most general setting possible by eliminating superfluous assumptions and by simplifying some of the conditions in statements. In this paper, we use…

As machine learning is increasingly used in essential systems, it is important to reduce or eliminate the incidence of serious bugs. A growing body of research has developed machine learning algorithms with formal guarantees about…

This note introduces the $\texttt{LikelihoodGeometry}$ package for the computer algebra system $\textit{Macaulay2}$. This package gives tools to construct the likelihood correspondence of a discrete algebraic statistical model, a variety…

We propose a new library to model and verify hardware circuits in the Coq proof assistant. This library allows one to easily build circuits by following the usual pen-and-paper diagrams. We define a deep-embedding: we use a (dependently…

With the emergence of Large Language Models (LLMs), there has been a significant improvement in the programming capabilities of models, attracting growing attention from researchers. Evaluating the programming capabilities of LLMs is…

This note is a response to Bas Spitter's email of 28 February 2014 about ML4PG: "We (Jason actually) are adding dependency graphs to our HoTT library: https://github.com/HoTT/HoTT/wiki I seem to recall that finding the dependency graph was…

Program refinement involves correctness-preserving transformations from formal high-level specification statements into executable programs. Traditional verification tool support for program refinement is highly interactive and lacks…

We introduce MLFMF, a collection of data sets for benchmarking recommendation systems used to support formalization of mathematics with proof assistants. These systems help humans identify which previous entries (theorems, constructions,…

In machine learning (ML) workflows, determining the invariance qualities of an ML model is a common testing procedure. Traditionally, invariance qualities are evaluated using simple formula-based scores, e.g., accuracy. In this paper, we…

We aim to automate decades of research and experience in register allocation, leveraging machine learning. We tackle this problem by embedding a multi-agent reinforcement learning algorithm within LLVM, training it with the state of the art…

We present a reflexive tactic for deciding the equational theory of Kleene algebras in the Coq proof assistant. This tactic relies on a careful implementation of efficient finite automata algorithms, so that it solves casual equations…

Formal verification via interactive theorem proving is increasingly used to ensure the correctness of critical systems, yet constructing large proof scripts remains highly manual and limits scalability. Advances in large language models…

We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns…

The increasing inclusion of Machine Learning (ML) models in safety critical systems like autonomous cars have led to the development of multiple model-based ML testing techniques. One common denominator of these testing techniques is their…

Modern advances in general-purpose computer algebra systems offer solutions to a variety of problems, which in the past required substantial time investments by trained mathematicians. An excellent example of such development are the…

Theorem proving is fundamental to program verification, where the automated proof of Verification Conditions (VCs) remains a primary bottleneck. Real-world program verification frequently encounters hard VCs that existing Automated Theorem…

Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called…

These are expanded lecture notes of a series of expository talks surveying basic aspects of group cohomology and homology. They were written for someone who has had a first course in graduate algebra but no background in cohomology. You…

Applying machine learning (ML) on multivariate time series data has growing popularity in many application domains, including in computer system management. For example, recent high performance computing (HPC) research proposes a variety of…

MLPACK is a state-of-the-art, scalable, multi-platform C++ machine learning library released in late 2011 offering both a simple, consistent API accessible to novice users and high performance and flexibility to expert users by leveraging…