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Large Language Models (LLMs) have recently achieved impressive performance in math and reasoning benchmarks. However, they often struggle with logic problems and puzzles that are relatively easy for humans. To further investigate this, we…

We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…

Program completion is a translation from the language of logic programs into the language of first-order theories. Its original definition has been extended to programs that include integer arithmetic, accept input, and distinguish between…

Solving complex, temporally-extended tasks is a long-standing problem in reinforcement learning (RL). We hypothesize that one critical element of solving such problems is the notion of compositionality. With the ability to learn concepts…

Generalized planning is about finding plans that solve collections of planning instances, often infinite collections, rather than single instances. Recently it has been shown how to reduce the planning problem for generalized planning to…

Large language models (LLMs) have demonstrated strong performance on formal language tasks, yet whether this reflects genuine symbolic reasoning or pattern matching on familiar constructions remains unclear. We introduce a benchmark for…

Cosine similarity between two words, computed using their contextualised token embeddings obtained from masked language models (MLMs) such as BERT has shown to underestimate the actual similarity between those words (Zhou et al., 2022).…

While large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, current benchmarks fail to adequately measure library-grounded abstraction -- the ability to reason with high-level interfaces and…

In this paper we show that reversible analysis of logic languages by abstract interpretation can be performed without loss of precision by systematically refining abstract domains. The idea is to include semantic structures into abstract…

We investigate the equational theory for Kleene algebra terms with variable complements and constant complements -- (language) complement where it applies only to variables or constants -- w.r.t. languages. While the equational theory…

Large language models (LLMs) are increasingly used for program verification, and yet little is known about \emph{how} they reason about program semantics during this process. In this work, we focus on abstract interpretation based-reasoning…

Reasoning requires going beyond pattern matching or memorization of solutions to identify and implement "algorithmic procedures" that can be used to deduce answers to hard problems. Doing so requires realizing the most relevant primitives,…

We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language -- which is the number of its (left) quotients, and…

The concept of causal abstraction got recently popularised to demystify the opaque decision-making processes of machine learning models; in short, a neural network can be abstracted as a higher-level algorithm if there exists a function…

Investigating deep learning language models has always been a significant research area due to the ``black box" nature of most advanced models. With the recent advancements in pre-trained language models based on transformers and their…

In this paper, we aim to establish a simple, effective, and theoretically grounded benchmark for rigorously probing abstract reasoning in Large Language Models (LLMs). To achieve this, we first develop a mathematic framework that defines…

Anomaly detection in computational workflows is critical for ensuring system reliability and security. However, traditional rule-based methods struggle to detect novel anomalies. This paper leverages large language models (LLMs) for…

During issue resolution, software developers rely on issue reports to discuss solutions for defects, feature requests, and other changes. These discussions contain proposed solutions--from design changes to code implementations--as well as…

Abstract interpretation is a method to automatically find invariants of programs or pieces of code whose semantics is given via least fixed-points. Up-to techniques have been introduced as enhancements of coinduction, an abstract principle…

We investigate the problem of segmenting unlabeled speech into word-like units and clustering these to create a lexicon. Prior work can be categorized into two frameworks. Bottom-up methods first determine boundaries and then cluster the…