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This work develops an LLM-based optimization framework ensuring strict constraint satisfaction in network optimization. While LLMs possess contextual reasoning capabilities, existing approaches often fail to enforce constraints, causing…

Augmenting large language models (LLMs) with external tools has emerged as a promising approach to solving complex problems. However, traditional methods, which finetune LLMs with tool demonstration data, can be both costly and restricted…

In this paper, we present our proposal to Constraint Functional Logic Programming over Finite Domains (CFLP(FD)) with a lazy functional logic programming language which seamlessly embodies finite domain (FD) constraints. This proposal…

Numerous real-world decision-making problems can be formulated and solved using Mixed-Integer Linear Programming (MILP) models. However, the transformation of these problems into MILP models heavily relies on expertise in operations…

Large language models are increasingly applied to operational decision-making where the underlying structure is constrained optimization. Existing benchmarks evaluate whether LLMs can formulate optimization problems as solver code, but…

Although unification can be used to implement a weak form of $\beta$-reduction, several linguistic phenomena are better handled by using some form of $\lambda$-calculus. In this paper we present a higher order feature description calculus…

We introduce MathConstraint, a hard, adaptive benchmark for evaluating the combinatorial reasoning capabilities of LLMs. We combine constraint satisfaction problems with rigorous solver-based verification and design an adaptive generator to…

Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework…

Large Language Models (LLMs) often exhibit limited logical coherence, mapping premises to conclusions without adherence to explicit inference rules. We propose Proof-Carrying Reasoning with LLMs (PCRLLM), a framework that constrains…

We solve an open problem related to an optimal encoding of a straight line program (SLP), a canonical form of grammar compression deriving a single string deterministically. We show that an information-theoretic lower bound for representing…

ACLP is a system which combines abductive reasoning and constraint solving by integrating the frameworks of Abductive Logic Programming (ALP) and Constraint Logic Programming (CLP). It forms a general high-level knowledge representation…

Large Language Models (LLMs) struggle with complex reasoning due to limited diversity and inefficient search. We propose Soft Reasoning, an embedding-based search framework that optimises the embedding of the first token to guide…

Concurrent programming often entails meticulous pairing of sends and receives between participants to avoid deadlock. Choreographic programming alleviates this burden by specifying the system as a single program. However, there are more…

The performance of multilingual pretrained models is highly dependent on the availability of monolingual or parallel text present in a target language. Thus, the majority of the world's languages cannot benefit from recent progress in NLP…

Reasoning over Commonsense Knowledge Bases (CSKB), i.e. CSKB reasoning, has been explored as a way to acquire new commonsense knowledge based on reference knowledge in the original CSKBs and external prior knowledge. Despite the advancement…

A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the…

Approximate linear programming (ALP) and its variants have been widely applied to Markov Decision Processes (MDPs) with a large number of states. A serious limitation of ALP is that it has an intractable number of constraints, as a result…

A minimal constructed language (conlang) is useful for experiments and comfortable for making tools. The Toki Pona (TP) conlang is minimal both in the vocabulary (with only 14 letters and 124 lemmas) and in the (about) 10 syntax rules. The…

We propose Modal Logical Neural Networks (MLNNs), a neurosymbolic framework that integrates deep learning with the formal semantics of modal logic, enabling reasoning about necessity and possibility. Drawing on Kripke semantics, we…

Discrete Combinatorial Problems (DCPs) are prevalent in industrial decision-making and optimisation. However, while constraint solving technologies for DCPs have advanced significantly, the core process of formalising them, namely…