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This paper presents Mathematical Execution (ME), a new, unified approach for testing numerical code. The key idea is to (1) capture the desired testing objective via a representing function and (2) transform the automated testing problem to…
We introduce a novel task consisting in assigning a proof to a given mathematical statement. The task is designed to improve the processing of research-level mathematical texts. Applying Natural Language Processing (NLP) tools to research…
Keeping in mind the necessity of intelligent system in educational sector, this paper proposes a text analysis based automated approach for automatic evaluation of the descriptive answers in an examination. In particular, the research…
Models of complicated systems can be represented in different ways - in scientific papers, they are represented using natural language text as well as equations. But to be of real use, they must also be implemented as software, thus making…
Digital mathematical libraries (DMLs) such as arXiv, Numdam, and EuDML contain mainly documents from STEM fields, where mathematical formulae are often more important than text for understanding. Conventional information retrieval (IR)…
We present iSMC, the first self-certifying model checker with interactive certification, a certification paradigm based on the theory of interactive proof systems. iSMC is a symbolic BDD-based model checker for arbitrary properties of…
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…
This article discusses a new technique to automatically generate test cases for object oriented programs. At the state of the art, the problem of generating adequate sets of complete test cases has not been satisfactorily solved yet. There…
The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous…
The last decade has seen tremendous progress in AI technology and applications. With such widespread adoption, ensuring the reliability of the AI models is crucial. In past, we took the first step of creating a testing framework called…
This paper provides the first correct semantical representation of UML state-machines within the logical framework of an institution (previous attempts were flawed). A novel encoding of this representation into first-order logic enables…
A prototype for an extensible interactive graphical term manipulation system is presented that combines pattern matching and nondeterministic evaluation to provide a convenient framework for doing tedious algebraic manipulations that so far…
Automated formalization of mathematics enables mechanical verification but remains limited to isolated theorems and short snippets. Scaling to textbooks and research papers is largely unaddressed, as it requires managing cross-file…
The purpose of the NIST Digital Repository of Mathematical Formulae (DRMF) is to create a digital compendium of mathematical formulae for orthogonal polynomials and special functions (OPSF) and of associated mathematical data. The DRMF…
Theorem proving is a fundamental task in mathematics. With the advent of large language models (LLMs) and interactive theorem provers (ITPs) like Lean, there has been growing interest in integrating LLMs and ITPs to automate theorem…
We present our vision for developing an automated tool capable of translating visual properties observed in Machine Learning (ML) visualisations into Python assertions. The tool aims to streamline the process of manually verifying these…
We consider the problem of symbolic-numeric integration of symbolic functions, focusing on rational functions. Using a hybrid method allows the stable yet efficient computation of symbolic antiderivatives while avoiding issues of…
Large language models have become proficient at generating functional code, but ensuring the output truly matches the programmer's intent remains difficult. Testing improves trust, yet for safety-critical applications, formal verification…
As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in…
Traditional approaches for validating molecular simulations rely on making software open source and transparent, incorporating unit testing, and generally employing human oversight. We propose an approach that eliminates software errors…