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We consider the recent formulation of the Algorithmic Lov\'asz Local Lemma [10,2,3] for finding objects that avoid `bad features', or `flaws'. It extends the Moser-Tardos resampling algorithm [17] to more general discrete spaces. At each…
LLM-based formal proof assistants (e.g., in Lean) hold great promise for automating mathematical discovery. But beyond syntactic correctness, do these systems truly understand mathematical structure as humans do? We investigate this…
The ability to automatically generalise (interactive) proofs and use such generalisations to discharge related conjectures is a very hard problem which remains unsolved. Here, we develop a notion of goal types to capture key properties of…
Data analysis and performance evaluation of simulation deduction plays a pivotal role in modern warfare, which enables military personnel to gain invaluable insights into the potential effectiveness of different strategies, tactics, and…
Materials discovery requires navigating vast chemical and structural spaces while satisfying multiple, often conflicting, objectives. We present LLM-guided Evolution for MAterials discovery (LLEMA), a unified framework that couples the…
Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of reasoning: efficiency. In real-world reasoning scenarios, much of the available…
Large Language Models (LLMs) have achieved remarkable capabilities, yet their improvement methods remain fundamentally constrained by human design. We present Self-Developing, a framework that enables LLMs to autonomously discover,…
Autoformalization, the process of transforming informal mathematical propositions into verifiable formal representations, is a foundational task in automated theorem proving, offering a new perspective on the use of mathematics in both…
Formal ontologies are axiomatizations in a logic-based formalism. The development of formal ontologies, and their important role in the Semantic Web area, is generating considerable research on the use of automated reasoning techniques and…
Abstract models of system-level behaviour have applications in design exploration, analysis, testing and verification. We describe a new algorithm for automatically extracting useful models, as automata, from execution traces of a HW/SW…
We present a reinforcement learning (RL) based guidance system for automated theorem proving geared towards Finding Longer Proofs (FLoP). Unlike most learning based approaches, we focus on generalising from very little training data and…
This entry contains the core material of my habilitation thesis, soon to be officially submitted. It provides a self-contained presentation of the original results in this thesis, in addition to their detailed proofs. The motivation of…
Induction lies at the heart of mathematics and computer science. However, automated theorem proving of inductive problems is still limited in its power. In this abstract, we first summarize our progress in automating inductive theorem…
We develop tools for analyzing focused stochastic local search algorithms. These are algorithms which search a state space probabilistically by repeatedly selecting a constraint that is violated in the current state and moving to a random…
Tractability results for the model checking problem of logics yield powerful algorithmic meta theorems of the form: Every computational problem expressible in a logic $L$ can be solved efficiently on every class $\mathscr{C}$ of structures…
Learning from demonstration is one of the most promising methods to counteract the challenging long-term trends in repetitive industrial assembly. It offers not only a programming technique that is accessible to workers on the shop floor,…
Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…
Combining different forms of prompts with pre-trained large language models has yielded remarkable results on reasoning tasks (e.g. Chain-of-Thought prompting). However, along with testing on more complex reasoning, these methods also…
LLMs face significant challenges in systematic generalization, particularly when dealing with reasoning tasks requiring compositional rules and handling out-of-distribution examples. To address these challenges, we introduce an in-context…
Recent advances in large language models (LLMs) have revolutionized the landscape of reasoning tasks. To enhance the capabilities of LLMs to emulate human reasoning, prior studies have focused on modeling reasoning steps using various…