Related papers: Pattern graph rewrite systems
E-graphs are a data structure that compactly represents equivalent expressions. They are constructed via the repeated application of rewrite rules. Often in practical applications, conditional rewrite rules are crucial, but their…
The theory of sequences, supported by many SMT solvers, can model program data types including bounded arrays and lists. Sequences are parameterized by the element data type and provide operations such as accessing elements, concatenation,…
The biological process of gene assembly has been modeled based on three types of string rewriting rules, called string pointer rules, defined on so-called legal strings. It has been shown that reduction graphs, graphs that are based on the…
Interaction nets are a form of restricted graph rewrite system that can serve as a graphical or textual programming language. As such, benefits include one-step confluence, ease of parallelism and explicit garbage collection. However, some…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
We review some of the recent developments in the construction of $W$-string theories. These are generalisations of ordinary strings in which the two-dimensional ``worldsheet'' theory, instead of being a gauging of the Virasoro algebra, is a…
Deep Recurrent Neural Network architectures, though remarkably capable at modeling sequences, lack an intuitive high-level spatio-temporal structure. That is while many problems in computer vision inherently have an underlying high-level…
We introduce a new class of graph transformation systems in which rewrite rules can be guarded by universally quantified conditions on the neighbourhood of nodes. These conditions are defined via special graph patterns which may be…
In the Matrix approach to graph transformation we represent simple digraphs and rules with Boolean matrices and vectors, and the rewriting is expressed using Boolean operators only. In previous works, we developed analysis techniques…
We develop a comprehensive string diagrammatic treatment of electrical circuits. Building on previous, limited case studies, we introduce controlled sources and meters as elements, and the impedance calculus, a powerful toolbox for…
This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a…
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different…
Many compilers, synthesizers, and theorem provers rely on rewrite rules to simplify expressions or prove equivalences. Developing rewrite rules can be difficult: rules may be subtly incorrect, profitable rules are easy to miss, and rulesets…
We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…
Graph neural networks (GNNs) are typically applied to static graphs that are assumed to be known upfront. This static input structure is often informed purely by insight of the machine learning practitioner, and might not be optimal for the…
String theories should reduce to ordinary four-dimensional field theories at low energies. Yet the formulation of the two are so different that such a connection, if it exists, is not immediately obvious. With the Schwinger proper-time…
We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern…
It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. Although most of…
We introduce a novel compositional description of Feynman diagrams, with well-defined categorical semantics as morphisms in a dagger-compact category. Our chosen setting is suitable for infinite-dimensional diagrammatic reasoning,…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…