Related papers: Filtrations of Formal Languages by Arithmetic Prog…
We give a simple, direct and reusable logical relations technique for languages with term and type recursion and partially defined differentiable functions. We demonstrate it by working out the case of Automatic Differentiation (AD)…
We present a simple technique for semantic, open logical relations arguments about languages with recursive types, which, as we show, follows from a principled foundation in categorical semantics. We demonstrate how it can be used to give a…
Prefix parsing asks whether an input prefix can be extended to a complete string generated by a given grammar. In the weighted setting, it also provides prefix probabilities, which are central to context-free language modeling,…
A self-similar algebra $\left(\mathfrak{A}, \psi \right)$ is an associative algebra $\mathfrak{A}$ with a morphism of algebras $\psi: \mathfrak{A} \longrightarrow M_d \left( \mathfrak{A}\right)$, where $M_d \left( \mathfrak{A}\right)$ is…
A recent study on structural properties of regular and context-free languages has greatly promoted our basic understandings of the complex behaviors of those languages. We continue the study to examine how regular languages behave when they…
Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different tools are being increasingly used in…
The hairpin completion is an operation on formal languages which is inspired by the hairpin formation in biochemistry. Hairpin formations occur naturally within DNA-computing. It has been known that the hairpin completion of a regular…
This paper defines a language L for specifying LFG grammars. This enables constraints on LFG's composite ontology (c-structures synchronised with f-structures) to be stated directly; no appeal to the LFG construction algorithm is needed. We…
Regular expressions in an Automata Theory and Formal Languages course are mostly treated as a theoretical topic. That is, to some degree their mathematical properties and their role to describe languages is discussed. This approach fails to…
We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational…
Morphological segmentation has traditionally been modeled with non-hierarchical models, which yield flat segmentations as output. In many cases, however, proper morphological analysis requires hierarchical structure -- especially in the…
We study canonical filtrations of finite-dimensional associative algebras and Lie algebras. These filtrations are defined via optimal destabilizing one-parameter subgroups in the sense of geometric invariant theory (GIT), and appear to be a…
Classifying formal languages according to the expressiveness of grammars able to generate them is a fundamental problem in computational linguistics and, therefore, in the theory of computation. Furthermore, such kind of analysis can give…
We introduce a class of convolutional neural networks (CNNs) that utilize recurrent neural networks (RNNs) as convolution filters. A convolution filter is typically implemented as a linear affine transformation followed by a non-linear…
We present a system for the automatic differentiation of a higher-order functional array-processing language. The core functional language underlying this system simultaneously supports both source-to-source automatic differentiation and…
We address the problem of segmenting an object given a natural language expression that describes it. Current techniques tackle this task by either (\textit{i}) directly or recursively merging linguistic and visual information in the…
In this paper we examine the limitations of Large Language Models (LLMs) for complex reasoning tasks. Although recent works have started to employ formal languages as an intermediate representation for reasoning tasks, they often face…
We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language -- the input of the problem -- and fixed language called filter is non-empty. In this paper we focus on the…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
Let $\Sigma = X\cup X^{-1} = \{ x_1 ,x_2 ,..., x_m ,x_1^{-1} ,x_2^{-1} ,..., x_m^{-1} \}$ and let $G$ be a group with set of generators $\Sigma$. Let $\mathfrak{L} (G) =\left\{ \left. \omega \in \Sigma^* \; \right\vert \;\omega \equiv e \;…