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The recently introduced framework of Graded Quantitative Rewriting is an innovative extension of traditional rewriting systems, in which rules are annotated with degrees drawn from a quantale. This framework provides a robust foundation for…
Linear integer constraints are one of the most important constraints in combinatorial problems since they are commonly found in many practical applications. Typically, encodings to Boolean satisfiability (SAT) format of conjunctive normal…
Quantizing large language models has become a standard way to reduce their memory and computational costs. Typically, existing methods focus on breaking down the problem into individual layer-wise sub-problems, and minimizing per-layer…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
With the recent advancements in deep learning, neural solvers have gained promising results in solving math word problems. However, these SOTA solvers only generate binary expression trees that contain basic arithmetic operators and do not…
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…
We provide a new foundational approach to the generalization of terms up to equational theories. We interpret generalization problems in a universal-algebraic setting making a key use of projective and exact algebras in the variety…
An arithmetic word problem typically includes a textual description containing several constant quantities. The key to solving the problem is to reveal the underlying mathematical relations (such as addition and subtraction) among…
The graph programming language GP 2 allows to apply sets of rule schemata (or "attributed" rules) non-deterministically. To analyse conflicts of programs statically, graphs labelled with expressions are overlayed to construct critical pairs…
Mitigating the hallucinations of Large Language Models is a crucial task. Although some existing methods employ self-enhancement techniques, they fall short of effectively addressing unknown factual hallucinations. Meanwhile, Knowledge…
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…
In this paper, we focus on computing local minimizers of a multivariate polynomial optimization problem under certain genericity conditions. By using a technique in computer algebra and the second-order optimality condition, we provide a…
This paper studies the unification problem with associative, commutative, and associative-commutative functions mainly from a viewpoint of the parameterized complexity on the number of variables. It is shown that both associative and…
We consider the embedding problem in coding theory: given an independence (a code-related property) and an independent language $L$, find a maximal independent language containing $L$. We consider the case where the code-related property is…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
Language models lack the notion of interchangeable tokens: symbols that are semantically equivalent yet distinct, such as bound variables in formal logic. This limitation prevents generalization to larger vocabularies and hinders the…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as…
Despite recent advancements in domain adaptation techniques for large language models, these methods remain computationally intensive, and the resulting models can still exhibit hallucination issues. Most existing adaptation methods do not…
Large Language Models (LLMs) showcase remarkable abilities, yet they struggle with limitations such as hallucinations, outdated knowledge, opacity, and inexplicable reasoning. To address these challenges, Retrieval-Augmented Generation…