Open Petri Nets

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 outputs of one to the inputs of another. Open Petri nets can be treated as morphisms of a category $\mathsf{Open}(\mathsf{Petri})$, which becomes symmetric monoidal under disjoint union. However, since the composite of open Petri nets is defined only up to isomorphism, it is better to treat them as morphisms of a symmetric monoidal double category $\mathbb{O}\mathbf{pen}(\mathsf{Petri})$. We describe two forms of semantics for open Petri nets using symmetric monoidal double functors out of $\mathbb{O}\mathbf{pen}(\mathsf{Petri})$. The first, an operational semantics, gives for each open Petri net a category whose morphisms are the processes that this net can carry out. This is done in a compositional way, so that these categories can be computed on smaller subnets and then glued together. The second, a reachability semantics, simply says which markings of the outputs can be reached from a given marking of the inputs.Comment: 30 pages, TikZ figure

Embroidery and artistic taste

Every aspect of art requires from a person the beauty of the heart, the elegance. One of the most ancient and unique types of applied decorative art is embroider

Master Snorer

Master Snorer is a fictional character corresponding to a nickname for the starring of a series of short stories published in Spanish Sociedad Española de Acústica under the name of Maestro Roncador in 2014. Master Snorer is a lecturer who educates Architecture students in the art of hear-ing in detail their environments, what improves, at a great extent, their professional abilities. Master Snorer´s life is explained through a series of stories corresponding to different moments in his life, and it is offered a sample from those stories as an application of ear-training in University studies in Architecture and Engineering.Postprint (published version