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Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…

Building mathematical optimization models is critical in operations research (OR), while it requires substantial human expertise. Recent advancements have utilized large language models (LLMs) to automate this modeling process. However,…

Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…

This document aims to be a self-contained, mathematically precise overview of transformer architectures and algorithms (*not* results). It covers what transformers are, how they are trained, what they are used for, their key architectural…

Proactive decision support (PDS) helps in improving the decision making experience of human decision makers in human-in-the-loop planning environments. Here both the quality of the decisions and the ease of making them are enhanced. In this…

Various software efforts embrace the idea that object oriented programming enables a convenient implementation of the chain rule, facilitating so-called automatic differentiation via backpropagation. Such frameworks have no mechanism for…

Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…

As predictive machine learning models become increasingly adopted and advanced, their role has evolved from merely predicting outcomes to actively shaping them. This evolution has underscored the importance of Trustworthy AI, highlighting…

Development of formal proofs of correctness of programs can increase actual and perceived reliability and facilitate better understanding of program specifications and their underlying assumptions. Tools supporting such development have…

Dynamic graph algorithms have seen significant theoretical advancements, but practical evaluations often lag behind. This work bridges the gap between theory and practice by engineering and empirically evaluating recently developed…

Solid modeling is a technique underlying CAD software as we see it today, and its theories and algorithms are among the most fundamental milestones in the historical development of CAD. Basically, it has answered the question of what…

From a set of technical drawings and expert knowledge, we automatically learn a parser to interpret such a drawing. This enables automatic reasoning and learning on top of a large database of technical drawings. In this work, we develop a…

Estimator algorithms in learning automata are useful tools for adaptive, real-time optimization in computer science and engineering applications. This paper investigates theoretical convergence properties for a special case of estimator…

In the nineties, several methods for dealing in a more efficient way with the implicitization of rational parametrizations were explored in the Computer Aided Geometric Design Community. The analysis of the validity of these techniques has…

Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…

Learning enabled autonomous systems provide increased capabilities compared to traditional systems. However, the complexity of and probabilistic nature in the underlying methods enabling such capabilities present challenges for current…

For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…

Many NLP applications require models to be interpretable. However, many successful neural architectures, including transformers, still lack effective interpretation methods. A possible solution could rely on building explanations from…

Software architecture knowledge transfer is essential for software development, but related documentation is often incomplete or ambiguous, making oral explanations a common means. Our broader aim is to explore how such explanations might…

Automatic translation of natural language mathematics into faithful Lean 4 code is hindered by the fundamental dissonance between informal set-theoretic intuition and strict formal type theory. This gap often causes LLMs to hallucinate…