Related papers: A unifying approach to picture grammars
In [BNRR], it was shown that tiling of general regions with two rectangles is NP-complete, except for a few trivial special cases. In a different direction, R\'emila showed that for simply connected regions by two rectangles, the…
We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
We present the stellar resolution, a "flexible" tile system based on Robinson's first-order resolution. After establishing formal definitions and basic properties of the stellar resolution, we show its Turing-completeness and to illustrate…
We propose a novel geometric approach for learning bilingual mappings given monolingual embeddings and a bilingual dictionary. Our approach decouples learning the transformation from the source language to the target language into (a)…
This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one…
Patterned self-assembly is a process whereby coloured tiles self-assemble to build a rectangular coloured pattern. We propose self-assembly (SA) hypergraph automata as an automata-theoretic model for patterned self-assembly. We investigate…
This paper presents a stochastic Wang tiling based technique to compress or reconstruct disordered microstructures on the basis of given spatial statistics. Unlike the existing approaches based on a single unit cell, it utilizes a finite…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…
Graphical languages are symmetric monoidal categories presented by generators and equations. The string diagrams notation allows to transform numerous axioms into low dimension topological rules we are comfortable with as three dimensional…
What does learning to model relationships between strings teach large language models (LLMs) about the visual world? We systematically evaluate LLMs' abilities to generate and recognize an assortment of visual concepts of increasing…
A graph $G = (V,E)$ is word-representable if there is a word $w$ over the alphabet $V$ such that $x$ and $y$ alternate in $w$ if and only if the edge $(x, y)$ is in $G$. It is known [6] that all $3$-colourable graphs are word-representable,…
How humans can effectively and efficiently acquire images has always been a perennial question. A classic solution is text-to-image retrieval from an existing database; however, the limited database typically lacks creativity. By contrast,…
An effort has been made to show mathematicians some new ideas applied to image analysis. Gray images are presented as tilings. Based on topological properties of the tiling, a number of gray convex hulls: maximal, minimal, and oriented ones…
Multimodal Large Language Models (MLLMs) have emerged as a promising foundation for universal multimodal embeddings. Recent studies have shown that reasoning-driven generative multimodal embeddings can outperform discriminative embeddings…
First we define a unification grammar formalism called the Tree Homomorphic Feature Structure Grammar. It is based on Lexical Functional Grammar (LFG), but has a strong restriction on the syntax of the equations. We then show that this…
Graph-based design languages in UML (Unified Modeling Language) are presented as a method to encode and automate the complete design process and the final optimization of the product or complex system. A design language consists of a…
Tidying up a messy table may appear simple for humans, but articulating clear criteria for tidiness is challenging due to the ambiguous nature of common sense reasoning. Large Language Models (LLMs) have proven capable of capturing common…
Reproducibility remains a cornerstone of scientific progress, yet complex multimodal models often lack transparent implementation details and accessible training infrastructure. In this work, we present a detailed reproduction and critical…
Framed combinatorial topology is a recent approach to tame geometry which expresses higher-dimensional stratified spaces via tractable combinatorial data. The resulting theory of spaces is well-behaved and computable. In this paper we…