Related papers: Morphisms of Coloured Petri Nets
We give a characterization of colored Petri nets as monoidal double functors. Framing colored Petri nets in terms of category theory allows for canonical definitions of various well-known constructions on colored Petri nets. In particular,…
The reachability semantics for Petri nets can be studied using open Petri nets. For us an "open" Petri net is one with certain places designated as inputs and outputs via a cospan of sets. We can compose open Petri nets by gluing the…
In this contribution we extend the concept of a Petri net morphism to Elementary Object Systems (EOS). EOS are a nets-within-nets formalism, i.e. we allow the tokens of a Petri net to be Petri nets again. This nested structure has the…
We present a formalism for Petri nets based on polynomial-style finite-set configurations and etale maps. The formalism supports both a geometric semantics in the style of Goltz and Reisig (processes are etale maps from graphs) and an…
We introduce a graphical calculus for computing morphism spaces between the categorified spin networks of Cooper and Krushkal. The calculus, phrased in terms of planar compositions of categorified Jones-Wenzl projectors and their duals, is…
Barwise and Seligman stated the first principle of information flow: "Information flow results from regularities in the distributed system." They represent a distributed system in terms of a classification consisting of a set of objects or…
Petri networks and network models are two frameworks for the compositional design of systems of interacting entities. Here we show how to combine them using the concept of a "catalyst": an entity that is neither destroyed nor created by any…
We inductively define layers of colorings of knot and knotted surface diagrams using ternary quasigroups. Homological invariants from such systems of colorings use shorter differentials and of higher degree than the standard homology…
Petri nets are a well-known model of concurrency and provide an ideal setting for the study of fundamental aspects in concurrent systems. Despite their simplicity, they still lack a satisfactory causally reversible semantics. We develop…
We extend the notion of graph homomorphism to cellularly embedded graphs (maps) by designing operations on vertices and edges that respect the surface topology; we thus obtain the first definition of map homomorphism that preserves both the…
Many categorical frameworks have been proposed to formalize the idea of gluing Petri nets with each other. Such frameworks model net gluings in terms of sharing of resources or synchronization of transitions. Interpretations given to these…
For every finite Petri net, we construct a commutative polynomial in two variables and with coefficients from the semiring of natural numbers. We also present an inverse construction and show that multiplication of polynomials…
A causal-net is a finite acyclic directed graph. In this paper, we introduce a category, denoted by $\mathbf{Cau}$ and called causal-net category, whose objects are causal-nets and morphisms between two causal-nets are the functors between…
Conformal nets are a mathematical model for conformal field theory, and defects between conformal nets are a model for an interaction or phase transition between two conformal field theories. In the preceding paper of this series, we…
This article presents formalistic tool for description of structural and biochemical relations between cells in the course of development of the body of plants. This is flexible formalistic space, based on the Category theory and the Petri…
Interlocking tables are the functional specification defining the routes on which the passage of the train is allowed. Associated with the route, the states and actions of all related signalling equipment are also specified. It is…
Petri nets are an established graphical formalism for modeling and analyzing the behavior of systems. An important consideration of the value of Petri nets is their use in describing both the syntax and semantics of modeling formalisms.…
We discuss the relationship between kernels, images and cokernels of morphisms between perverse sheaves and induced maps on stalk cohomology.
The notion of proof-net category defined in this paper is closely related to graphs implicit in proof nets for the multiplicative fragment without constant propositions of linear logic. Analogous graphs occur in Kelly's and Mac Lane's…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…