Related papers: E-Graphs With Bindings
This thesis proposes an advanced, generic and high-level code rewriting and analysis system in the Julia programming language, providing applied equality saturation in the presence of multiple dispatch and metaprogramming. We show how our…
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…
Term graph rewriting is important as "conceptual implementation" of the execution of functional programs, and of data-flow optimisations in compilers. One way to define term graph transformation rule application is via the well-established…
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…
Critical pair analysis provides a convenient and computable criterion of confluence, which is a fundamental property in rewriting theory, for a wide variety of rewriting systems. Bonchi et al. showed validity of critical pair analysis for…
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…
Threshold graphs are recursive deterministic network models that have been proposed for describing certain economic and social interactions. One drawback of this graph family is that it has limited generative attachment rules. To mitigate…
We study rewriting for equational theories in the context of symmetric monoidal categories where there is a separable Frobenius monoid on each object. These categories, also called hypergraph categories, are increasingly relevant: Frobenius…
We extend the powerful Pullback-Pushout (PBPO) approach for graph rewriting with strong matching. Our approach, called \pbpostrong, exerts more control over the embedding of the pattern in the host graph, which is important for a large…
Context: Edge graphs are graphs whose edges are labelled with identifiers, and nodes can have multiple edges between them. They are used to model a wide range of systems, including networks with distances or degrees of connection and…
Given a graph $G$, a vertex switch of $v \in V(G)$ results in a new graph where neighbors of $v$ become nonneighbors and vice versa. This operation gives rise to an equivalence relation over the set of labeled digraphs on $n$ vertices. The…
Term Rewriting Systems (TRSs) are used in compilers to simplify and prove expressions. State-of-the-art TRSs in compilers use a greedy algorithm that applies a set of rewriting rules in a predefined order (where some of the rules are not…
With a view on applications in computing, in particular concurrency theory and higher-dimensional rewriting, we develop notions of $n$-fold monoid and comonoid objects in $n$-fold monoidal categories and bicategories. We present a series of…
Graphs, such as social networks, word co-occurrence networks, and communication networks, occur naturally in various real-world applications. Analyzing them yields insight into the structure of society, language, and different patterns of…
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,…
Word-representable graphs, which are the same as semi-transitively orientable graphs, generalize several fundamental classes of graphs. In this paper we propose a novel approach to study word-representability of graphs using a technique of…
Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the…
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph…
Narrowing is a well-known technique that adds to term rewriting mechanisms the required power to search for solutions to equational problems. Rewriting and narrowing are well-studied in first-order term languages, but several problems…
We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is…