Related papers: A unifying approach to picture grammars
A recognizable picture language is defined as the projection of a local picture language defined by a set of two-by-two tiles, i.e. by a strictly-locally-testable (SLT) language of order 2. The family of recognizable picture languages is…
Tiling recognizable two-dimensional languages, also known as REC, generalize recognizable string languages to two dimensions and share with them several theoretical properties. Nevertheless REC is not closed under complementation and the…
We over-approximate reachability sets in string rewriting by languages defined by admissible factors, called tiles. A sparse set of tiles contains only those that are reachable in derivations, and is constructed by completing an automaton.…
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
In a recent paper, Altenbernd, Thomas and W\"ohrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the B\"uchi and Muller…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
Study of patterns on images is recognized as an important step in characterization and classification of image. The ability to efficiently analyze and describe image patterns is thus of fundamental importance. The study of syntactic methods…
Image-text retrieval aims to bridge the modality gap and retrieve cross-modal content based on semantic similarities. Prior work usually focuses on the pairwise relations (i.e., whether a data sample matches another) but ignores the…
A basic assumption of tiling theory is that adjacent tiles can meet in only a finite number of ways, up to rigid motions. However, there are many interesting tiling spaces that do not have this property. They have "fault lines", along which…
Multimodal models are becoming increasingly effective, in part due to unified components, such as the Transformer architecture. However, multimodal models still often consist of many task- and modality-specific pieces and training…
We consider a certain tiling problem of a planar region in which there are no long horizontal or vertical strips consisting of copies of the same tile. Intuitively speaking, we would like to create a dappled pattern with two or more kinds…
In this extended abstract, we present a simple approach to convergence on term graphs that allows us to unify term graph rewriting and infinitary term rewriting. This approach is based on a partial order and a metric on term graphs. These…
Altenbernd, Thomas and W\"ohrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with usual acceptance conditions, such as the B\"uchi and Muller ones [1]. It was proved…
In this article, we present a fresh perspective on language, combining ideas from various sources, but mixed in a new synthesis. As in the minimalist program, the question is whether we can formulate an elegant formalism, a universal…
In this paper, we introduce a generalization of a class of tilings which appear in the literature: the tilings over which a height function can be defined (for example, the famous tilings of polyominoes with dominoes). We show that many…
The Wang tiling is a classical problem in combinatorics. A major theoretical question is to find a (small) set of tiles which tiles the plane only aperiodically. In this case, resulting tilings are rather restrictive. On the other hand,…
Tilings of the plane resemble the simplicial and other complexes from algebraic topology, but have not been studied from this perspective. We construct finite categories corresponding to polygons with labeled directed edges, and introduce…
Existing vision-language methods typically support two languages at a time at most. In this paper, we present a modular approach which can easily be incorporated into existing vision-language methods in order to support many languages. We…
This paper provides a bridge between the classical tiling theory and the complex neighborhood self-assembling situations that exist in practice. The neighborhood of a position in the plane is the set of coordinates which are considered…
The tiling problem has been a famous problem that has appeared in many Mathematics problems. Many of its solutions are rooted in high-level Mathematics. Thus we hope to tackle this problem using more elementary Mathematics concepts. In this…