Related papers: Towards 3-Dimensional Rewriting Theory
Programs offer compactness and structure that makes them an attractive representation for visual data. We explore how code rewriting can be used to improve systems for inferring programs from visual data. We first propose Sparse…
The vast amount of data and increase of computational capacity have allowed the analysis of texts from several perspectives, including the representation of texts as complex networks. Nodes of the network represent the words, and edges…
An important way for describing groups is by finite presentations. Large presentations arise in practice which are poorly suited for either human or computer use. Presentation simplification processes which take bad presentations and…
This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…
Multiset rewriting systems provide a formalism particularly suitable for the description of biological systems. We present an extension of this formalism with additional controls on the derivations as a tool for reducing possible…
We study the notion of hierarchy in the context of visualizing textual data and navigating text collections. A formal framework for ``hierarchy'' is given by an ultrametric topology. This provides us with a theoretical foundation for…
This work introduces Bilinear Classes, a new structural framework, which permit generalization in reinforcement learning in a wide variety of settings through the use of function approximation. The framework incorporates nearly all existing…
Adhesive categories provide an abstract framework for the algebraic approach to rewriting theory, where many general results can be recast and uniformly proved. However, checking that a model satisfies the adhesivity properties is sometimes…
We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…
Reproducibility has been increasingly encouraged by communities of science in order to validate experimental conclusions, and replication studies represent a significant opportunity to vision scientists wishing contribute new perceptual…
This paper contains the results collected so far on polynomial composites in terms of many basic algebraic properties. Since it is a polynomial structure, results for monoid domains come in here and there. The second part of the paper…
Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure.…
Hypergraphs, or generalization of graphs such that edges can contain more than two nodes, have become increasingly prominent in understanding complex network analysis. Unlike graphs, hypergraphs have relatively few supporting platforms, and…
We introduce a novel type of text representation that preserves the 2D layout of a document. This is achieved by encoding each document page as a two-dimensional grid of characters. Based on this representation, we present a generic…
A basic experiment in probability theory is drawing without replacement from an urn filled with multiple balls of different colours. Clearly, it is physically impossible to overdraw, that is, to draw more balls from the urn than it…
The intention of the present study is to establish general framework for automated problem solving by approaching the task universal algebraically introducing knowledge as realizations of generalized free algebra based nets, graphs with…
In traditional rewriting theory, one studies a set of terms up to a set of rewriting relations. In algebraic rewriting, one instead studies a vector space of terms, up to a vector space of relations. Strikingly, although both theories are…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
This paper proposes a new class of multi-dimensional nonsystematic Reed-Solomon codes that are constructed based on the multi-dimensional Fourier transform over a finite field. The proposed codes are the extension of the nonsystematic…
E-graphs are a data structure for equational reasoning and optimization over ground terms. One of the benefits of e-graph rewriting is that it can declaratively handle useful but difficult to orient identities like associativity and…