Related papers: Foundations of brick diagrams

Central to near-term quantum machine learning is the use of hybrid quantum-classical algorithms. This paper develops a formal framework for describing these algorithms in terms of string diagrams: a key step towards integrating these hybrid…

String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less…

Object Oriented Data Analysis is a new area in statistics that studies populations of general data objects. In this article we consider populations of tree-structured objects as our focus of interest. We develop improved analysis tools for…

Bimonoidal categories (also known as rig categories) are categories with two monoidal structures, one of which distributes over the other. We formally define sheet diagrams, a graphical calculus for bimonoidal categories that was informally…

Milner's bigraphs are a general framework for reasoning about distributed and concurrent programming languages. Notably, it has been designed to encompass both the pi-calculus and the Ambient calculus. This paper is only concerned with…

Proof nets are a syntax for linear logic proofs which gives a coarser notion of proof equivalence with respect to syntactic equality together with an intuitive geometrical representation of proofs. In this paper we give an alternative…

Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…

We introduce the notion of a braiding on a skew monoidal category, whose curious feature is that the defining isomorphisms involve three objects rather than two. These braidings are shown to arise from, and classify, cobraidings (also known…

Equational reasoning with string diagrams provides an intuitive means of proving equations between morphisms in a symmetric monoidal category. This can be extended to proofs of infinite families of equations using a simple graphical syntax…

We revisit the problem of hard particles on planar random tetravalent graphs in view of recent combinatorial techniques relating planar diagrams to decorated trees. We show how to recover the two-matrix model solution to this problem in…

Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…

This paper explores the kinds of probabilistic relations that are important in syntactic disambiguation. It proposes that two widely used kinds of relations, lexical dependencies and structural relations, have complementary disambiguation…

We present a Rocq library for monoidal categories, which includes a decision procedure for proving equality of morphisms as well as notations that make it possible to reason as if they were strict, inferring MacLane isomorphims…

String diagrams are a powerful and intuitive graphical syntax, originated in the study of symmetric monoidal categories. In the last few years, they have found application in the modelling of various computational structures, in fields as…

Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…

Parse trees are fundamental syntactic structures in both computational linguistics and compilers construction. We argue in this paper that, in both fields, there are good incentives for model-checking sets of parse trees for some word…

Data structures known as $k$-d trees have numerous applications in scientific computing, particularly in areas of modern statistics and data science such as range search in decision trees, clustering, nearest neighbors search, local…

We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…

We propose a graphical language that accommodates two monoidal structures: a multiplicative one for pairing and an additional one for branching. In this colored PROP, whether wires in parallel are linked through the multiplicative structure…

In reliability engineering, we need to understand system dependencies, cause-effect relations, identify critical components, and analyze how they trigger failures. Three prominent graph models commonly used for these purposes are fault…