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Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…
A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models. To tackle this problem, we propose an approach that relies…
Program verifiers such as Dafny automate proofs by outsourcing them to an SMT solver. This automation is not perfect, however, and the solver often requires hints in the form of assertions, creating a burden for the proof engineer. In this…
Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…
We present VERIFAI, a software toolkit for the formal design and analysis of systems that include artificial intelligence (AI) and machine learning (ML) components. VERIFAI particularly seeks to address challenges with applying formal…
The current verification flow of complex systems uses different engines synergistically: virtual prototyping, formal verification, simulation, emulation and FPGA prototyping. However, none is able to verify a complete architecture.…
Highly automated theorem provers like Dafny allow users to prove simple properties with little effort, making it easy to quickly sketch proofs. The drawback is that such provers leave users with little control about the proof search,…
Over the past 27 years, quantum computing has seen a huge rise in interest from both academia and industry. At the current rate, quantum computers are growing in size rapidly backed up by the increase of research in the field. Significant…
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…
We report about significant enhancements of the complex algebraic geometry theorem proving subsystem in GeoGebra for automated proofs in Euclidean geometry, concerning the extension of numerous GeoGebra tools with proof capabilities. As a…
During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical…
Many scientific disciplines have traditionally advanced by iterating over hypotheses using labor-intensive trial-and-error, which is a slow and expensive process. Recent advances in computing, digitalization, and machine learning have…
Can artificial intelligence truly contribute to creative mathematical research, or does it merely automate routine calculations while introducing risks of error? We provide empirical evidence through a detailed case study: the discovery of…
We describe in a rudimentary fashion how SVM(support vector machine) plays the role of classifier in a mathematical setting. We then discuss its application in the study of multiple SNP(single nucleotide polymorphism) variations. Also…
Model checking and automated theorem proving are two pillars of formal methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and…
Artificial intelligence (AI) is transforming the practice of science. Machine learning and large language models (LLMs) can generate hypotheses at a scale and speed far exceeding traditional methods, offering the potential to accelerate…
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…
Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…
Advances in foundation modeling have reshaped computational pathology. However, the increasing number of available models and lack of standardized benchmarks make it increasingly complex to assess their strengths, limitations, and potential…
Software verification is a tedious process that involves the analysis of multiple failed verification attempts, and adjustments of the program or specification. This is especially the case for complex requirements, e.g., regarding security…