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We report on our experiments to train deep neural networks that automatically translate informalized LaTeX-written Mizar texts into the formal Mizar language. To the best of our knowledge, this is the first time when neural networks have…

We present a methodology for the automated verification of quantum protocols using MCMAS, a symbolic model checker for multi-agent systems The method is based on the logical framework developed by D'Hondt and Panangaden for investigating…

This paper presents an automated tool called Morphy for datamorphic testing. It classifies software test artefacts into test entities and test morphisms, which are mappings on testing entities. In addition to datamorphisms, metamorphisms…

Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…

Retrieving mathematical knowledge is a central task in both human-driven research, such as determining whether a result already exists, finding related results, and identifying historical origins, and in emerging AI systems for mathematics,…

Formal mathematical reasoning remains a critical challenge for artificial intelligence, hindered by limitations of existing benchmarks in scope and scale. To address this, we present FormalMATH, a large-scale Lean4 benchmark comprising…

Formal proofs are challenging to write even for experienced experts. Recent progress in Neural Theorem Proving (NTP) shows promise in expediting this process. However, the formal corpora available on the Internet are limited compared to the…

Systematic development of accurate density functionals has been a decades-long challenge for scientists. Despite the emerging application of machine learning (ML) in approximating functionals, the resulting ML functionals usually contain…

While the ecosystem of Lean and Mathlib has enjoyed celebrated success in formal mathematical reasoning with the help of large language models (LLMs), the absence of many folklore lemmas in Mathlib remains a persistent barrier that limits…

The refinement calculus provides a methodology for transforming an abstract specification into a concrete implementation, by following a succession of refinement rules. These rules have been mechanized in theorem-provers, thus providing a…

Over the last few decades, many distinct lines of research aimed at automating mathematics have been developed, including computer algebra systems (CASs) for mathematical modelling, automated theorem provers for first-order logic, SAT/SMT…

Automated testing plays a crucial role in ensuring software security. It heavily relies on formal specifications to validate the correctness of the system behavior. However, the main approach to defining these formal specifications is…

In this paper, we present a new approach to the semantic enrichment of mathematical expression problem. Our approach is a combination of statistical machine translation and disambiguation which makes use of surrounding text of the…

It is the aim of this work to identify and illustrate the potential and weaknesses of the computer algebra system Maple in the area of the Calculus of Variations: a classical area of mathematics that studies the methods for finding maximum…

Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's…

Modern Large Language Model (LLM)-based programming agents often rely on test execution feedback to refine their generated code. These tests are synthetically generated by LLMs. However, LLMs may produce invalid or hallucinated test cases,…

Intuitively, an (implementation) automata is simulated by a (specification) automata if every externally observable transition by the implementation automata can also be made by the specification automata. In this work, we present a…

Finite Automata (FAs) are fundamental components in the domains of programming languages. For instance, regular expressions, which are pivotal in languages such as JavaScript and Python, are frequently implemented using FAs. Finite…

We provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when their arguments are rational functions. These algorithms are implemented in Maple and we…

Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis,…