Related papers: Rewriting in Gray categories with applications to …

In rule-based systems, goal-oriented computations correspond naturally to the possible ways that an observation may be explained. In some applications, we need to compute explanations for a series of observations with the same domain. The…

We show how the notion of intercategory encompasses a wide variety of three-dimensional structures from the literature, notably duoidal categories, monoidal double categories, cubical bicategories, double bicategories and Gray categories.…

We describe a mathematical framework for equational reasoning about infinite families of string diagrams which is amenable to computer automation. The framework is based on context-free families of string diagrams which we represent using…

We introduce acyclic polygraphs, a notion of complete categorical cellular model for (small) categories, containing generators, relations and higher-dimensional globular syzygies. We give a rewriting method to construct explicit acyclic…

This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…

The role of types in categorical models of meaning is investigated. A general scheme for how typed models of meaning may be used to compare sentences, regardless of their grammatical structure is described, and a toy example is used as an…

Windowed recurrences are sliding window calculations where a function is applied iteratively across the window of data, and are ubiquitous throughout the natural, social, and computational sciences. In this monograph we explore the…

The relationship between Term Graph Rewriting and Term Rewriting is well understood: a single term graph reduction may correspond to several term reductions, due to sharing. It is also known that if term graphs are allowed to contain…

We establish two versions of a central theorem, the Family Colimit Theorem, for the coarse coherence property of metric spaces. This is a coarse geometric property and so is well-defined for finitely generated groups with word metrics. It…

Typical arguments for results like Kleene's Second Recursion Theorem and the existence of self-writing computer programs bear the fingerprints of equational reasoning and combinatory logic. In fact, the connection of combinatory logic and…

In this paper we present $2$-category theory from the perspective of Gray-categories using the graphical calculus of separated surface diagrams. As an extended example we consider cones and limits of $2$-functors. Then we use the canonical…

First formally defined by Borodin and Olshanski, a coherent system on a graded graph is a sequence of probability measures which respect the action of certain down/up transition functions between graded components. In one common example of…

A complementary Gray code for binary n-tuples is one that, when all the tuples are complemented, is identical to itself; this is equivalent to the complement of the first half of the code being identical to the second half. We generalize…

Equality saturation, a technique for program optimisation and reasoning, has gained attention due to the resurgence of equality graphs (e-graphs). E-graphs represent equivalence classes of terms under rewrite rules, enabling simultaneous…

In a Systems Engineering setting, various models are produced using a variety of methods and tools. Focusing on a type of models -- called descriptive models -- which we shall describe, we argue that, while the clarity and precision of…

We introduce a class of rooted graphs which allows one to encode various kinds of classical or quantum circuits. We then follow a set-theoretic approach to define rewrite systems over the considered graphs and propose a new complete…

We study rewriting systems whose underlying set of terms is equipped with a vector space structure over a given field. We introduce parallel rewriting relations, which are rewriting relations compatible with the vector space structure, as…

We examine a variant of hypergraphs that we call interfaced linear hypergraphs, with the aim of creating a sound and complete graphical language for symmetric traced monoidal categories (STMCs) suitable for graph rewriting. In particular,…

Bayesian Filtering for plan and activity recognition is challenging for scenarios that contain many observation equivalent entities (i.e. entities that produce the same observations). This is due to the combinatorial explosion in the number…

Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…