Related papers: The Algebra of Open and Interconnected Systems

Let $\mathcal C$ be a category with finite colimits, writing its coproduct $+$, and let $(\mathcal D, \otimes)$ be a braided monoidal category. We describe a method of producing a symmetric monoidal category from a lax braided monoidal…

We address the problem of defining connected components in hypergraphs, which are models for systems with higher-order interactions. For graphs with dyadic interactions, connected components are defined in terms of paths connecting nodes…

We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the Configuration Model where nodes of different types are connected via…

Naturally occurring diagrams in algebraic topology are commutative up to homotopy, but not on the nose. It was quickly realized that very little can be done with this information. Homotopy coherent category theory arose out of a desire to…

In this paper we adapt previous work on rewriting string diagrams using hypergraphs to the case where the underlying category has a traced comonoid structure, in which wires can be forked and the outputs of a morphism can be connected to…

Digital circuits, despite having been studied for nearly a century and used at scale for about half that time, have until recently evaded a fully compositional theoretical in which arbitrary circuits may be freely composed together without…

Patterns stored within pre-trained deep neural networks compose large and powerful descriptive languages that can be used for many different purposes. Typically, deep network representations are implemented within vector embedding spaces,…

Distributional learning provides a framework for studying the learnability of structured languages from positive data. In this paper, we extend this framework to graph languages generated by fixed-interface clause systems. We formulate…

We present a computational implementation of diagrammatic sets, a model of higher-dimensional diagram rewriting that is "topologically sound": diagrams admit a functorial interpretation as homotopies in cell complexes. This has potential…

A functional hardware description language enables students to gain a working understanding of computer systems, and to see how the levels of abstraction fit together. By simulating circuits, digital design becomes a living topic, like…

As a crucial step in extractive document summarization, learning cross-sentence relations has been explored by a plethora of approaches. An intuitive way is to put them in the graph-based neural network, which has a more complex structure…

Thanks to the availability of large scale digital datasets and massive amounts of computational power, deep learning algorithms can learn representations of data by exploiting multiple levels of abstraction. These machine learning methods…

These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over…

The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The complete Prolog code is available at…

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)}…

It is evident that the current state of Large Language Models (LLMs) necessitates the incorporation of external tools. The lack of straightforward algebraic and logical reasoning is well documented and prompted researchers to develop…

This short paper examines diagrams describing neural network systems in academic conference proceedings. Many aspects of scholarly communication are controlled, particularly with relation to text and formatting, but often diagrams are not…

In many real-world networks, nodes have class labels, attributes, or variables that affect the network's topology. If the topology of the network is known but the labels of the nodes are hidden, we would like to select a small subset of…

Observing a set of images and their corresponding paragraph-captions, a challenging task is to learn how to produce a semantically coherent paragraph to describe the visual content of an image. Inspired by recent successes in integrating…

Message Sequence Charts & Sequence Diagrams are graphical models that represent the behavior of distributed and concurrent systems via the scheduling of discrete and local emission and reception events. We propose an Interaction Language…