Related papers: A Critical Pair Enumeration Algorithm for String D…

Graph rewriting is a popular tool for the optimisation and modification of graph expressions in domains such as compilers, machine learning and quantum computing. The underlying data structures are often port graphs - graphs with labels at…

Confluence is a fundamental property of Constraint Handling Rules (CHR) since, as in other rewriting formalisms, it guarantees that the computations are not dependent on rule application order, and also because it implies the logical…

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating…

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…

With the popularization of Topological Data Analysis, the Reeb graph has found new applications as a summarization technique in the analysis and visualization of large and complex data, whose usefulness extends beyond just the graph itself.…

The string-matching field has grown at a such complicated stage that various issues come into play when studying it: data structure and algorithmic design, database principles, compression techniques, architectural features, cache and…

We tackle the problem of attributed graph transformations and propose a new algorithmic approach for defining parallel graph transformations allowing overlaps. We start by introducing some abstract operations over graph structures. Then, we…

Coherence theorems for covariant structures carried by a category have traditionally relied on the underlying term rewriting system of the structure being terminating and confluent. While this holds in a variety of cases, it is not a…

The aim of this thesis is to present an extension to the string graphs of Dixon, Duncan and Kissinger that allows the finite representation of certain infinite families of graphs and graph rewrite rules, and to demonstrate that a logic can…

We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…

A string diagram is a two-dimensional graphical representation that can be described as a one-dimensional term generated from a set of primitives using sequential and parallel compositions. Since different syntactic terms may represent the…

The problem of reconstructing strings from their substring spectra has a long history and in its most simple incarnation asks for determining under which conditions the spectrum uniquely determines the string. We study the problem of coded…

The Critical Node Problem (CNP) is to identify a subset of nodes in a graph whose removal maximally degrades pairwise connectivity. The CNP is an important variant of the Critical Node Detection Problem (CNDP) with wide applications. Due to…

String diagrams are a graphical language used to represent processes that can be composed sequentially or in parallel, which correspond graphically to horizontal or vertical juxtaposition. In this paper we demonstrate how to compute the…

Diagram chasing is not an easy task. The coherence holds in a generalized sense if we have a mechanical method to judge whether given two morphisms are equal to each other. A simple way to this end is to reform a concerned category into a…

We study the combination of the following already known ideas for showing confluence of unconditional or conditional term rewriting systems into practically more useful confluence criteria for conditional systems: Our syntactical separation…

Higher-dimensional rewriting is founded on a duality of rewrite systems and cell complexes, connecting computational mathematics to higher categories and homotopy theory: the two sides of a rewrite rule are two halves of the boundary of an…

Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence. This fact, however, is meaningful in restricted cases only, depending on the shape of the sentence…

We introduce a categorical formalism for rewriting surface-embedded graphs. Such graphs can represent string diagrams in a non-symmetric setting where we guarantee that the wires do not intersect each other. The main technical novelty is a…

Intersection graphs are well-studied in the area of graph algorithms. Some intersection graph classes are known to have algorithms enumerating all unlabeled graphs by reverse search. Since these algorithms output graphs one by one and the…