Related papers: The operad of wiring diagrams: formalizing a graph…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
Reusing verification artefacts requires identifying structural and semantic similarities across programs and their specifications. In this paper, we focus on graph construction as a foundational step toward this goal. We present a pipeline…
The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
Modular operads are a special type of operad: in fact, they bear the same relationship to operads that graphs do to trees (i.e. simply connected graphs). One of the basic examples of a modular operad is the collection of…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
Operads may be represented as symmetric monoidal functors on a small symmetric monoidal category. We discuss the axioms which must be imposed on a symmetric monoidal functor in order that it give rise to a theory similar to the theory of…
In this article, we describe how coalgebraic structures on operads induce algebraic structures on their categories of algebras and coalgebras.
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
This paper presents a detailed symbolic approach to the study of self-similar tilings. It uses properties of addresses associated with graph-directed iterated function systems to establish conjugacy properties of tiling spaces. Tiles may be…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
This paper gives an explicit description of the categorical operad whose algebras are precisely symmetric monoidal categories. This allows us to place the operad in a sequence of four, and therefore a sequence of four successively stricter…
Circuit diagrams have been used in electrical engineering for decades to describe the wiring of devices and facilities. They depict electrical components in a symbolic and graph-based manner. While the circuit design is usually performed…
We study the divided power structures over a product of operads with distributive law. We give a systematic method to characterise the divided power algebras over such a product from the structures of divided power algebra coming from each…
Many topological data analysis (TDA) pipelines compute large collections of persistence diagrams, yet vectorizations and kernel methods discard the rank-induced implication relations among persistence intervals that are essential for…
Graph grammars extend the theory of formal languages in order to model distributed parallelism in theoretical computer science. We show here that to certain classes of context-free and context-sensitive graph grammars one can associate a…
We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures…
Railroad diagrams (also called "syntax diagrams") are a common, intuitive visualization of grammars, but limited tooling and a lack of formal attention to their layout mostly confines them to hand-drawn documentation. We present the first…
Diagrams matter. Unfortunately, the deep learning community has no standard method for diagramming architectures. The current combination of linear algebra notation and ad-hoc diagrams fails to offer the necessary precision to understand…
This document reports on the use of an algebraic, visual, formal approach to the specification of patterns for the formalization of the GoF design patterns. The approach is based on graphs, morphisms and operations from category theory and…