Related papers: A unifying approach to picture grammars
Matrix Graph Grammars (MGG) is a novel approach to the study of graph dynamics ([15]). In the present contribution we look at MGG as a formal grammar and as a model of computation, which is a necessary step in the more ambitious program of…
While a great effort has concerned the development of fully integrated modular understanding systems, few researches have focused on the problem of unifying existing linguistic formalisms with cognitive processing models. The Situated…
Image classification is an essential part of computer vision which assigns a given input image to a specific category based on the similarity evaluation within given criteria. While promising classifiers can be obtained through deep…
The paper explains the connection between topological theories for one-manifolds with defects and values in the Boolean semiring and automata and their generalizations. Finite state automata are closely related to regular languages. To each…
State-of-the-art learned reconstruction methods often rely on black-box modules that, despite their strong performance, raise questions about their interpretability and robustness. Here, we build on a recently proposed image reconstruction…
It is well-known that the question of whether a given finite region can be tiled with a given set of tiles is NP-complete. We show that the same is true for the right tromino and square tetromino on the square lattice, or for the right…
Grammar refers to the system of rules that governs the structural organization and the semantic relations among linguistic units such as sentences, phrases, and words within a given language. In natural language processing, there remains a…
Existing technology can parse arbitrary context-free grammars, but only a single, static grammar per input. In order to support more powerful syntax-extension systems, we propose reflective grammars, which can modify their own syntax during…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
A categorial grammar assigns one of several syntactic categories to each symbol of the alphabet, and the category of a string is then deduced from the categories assigned to its symbols using two simple reduction rules. This paper…
Square-triangle-rhombus ($\mathcal{STR}$) tilings are encountered in various self-organized multi-component systems. They exhibit a rich structural diversity, encompassing both periodic tilings and long-range ordered quasicrystals,…
The rise of multi-paradigm languages challenges traditional classification methods, leading to practical software engineering issues like interoperability defects. This systematic literature review (SLR) maps the formal foundations of…
Every simple quadrangulation of the sphere is generated by a graph called a pseudo-double wheel with two local expansions (Brinkmann et al. "Generation of simple quadrangulations of the sphere." Discrete Math., Vol. 305, No. 1-3, pp. 33-54,…
The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…
We propose a concrete surface representation of abstract categorial grammars in the category of word cobordisms or cowordisms for short, which are certain bipartite graphs decorated with words in a given alphabet, generalizing linear logic…
We pose 3D scene-understanding as a problem of parsing in a grammar. A grammar helps us capture the compositional structure of real-word objects, e.g., a chair is composed of a seat, a back-rest and some legs. Having multiple rules for an…
We extend rotation theory of circle maps to tiling spaces. Specifically, we consider a 1-dimensional tiling space $\Omega$ with finite local complexity and study self-maps $F$ that are homotopic to the identity and whose displacements are…
We introduce regular languages of morphisms in free monoidal categories, with their associated grammars and automata. These subsume the classical theory of regular languages of words and trees, but also open up a much wider class of…
With the proliferation of image-based applications in various domains, the need for accurate and interpretable image similarity measures has become increasingly critical. Existing image similarity models often lack transparency, making it…
We first recall some basic notions on minimalist grammars and on categorial grammars. Next we shortly introduce partially commutative linear logic, and our representation of minimalist grammars within this categorial system, the so-called…