Algebra/Topology Seminar

Speaker: Joachim Kock

Title: Petri nets and processes

Abstract: Petri nets are a very useful formalism for modelling processes, with
applications in many different fields of science and engineering
such as chemistry, epidemiology, computer science, and business and
production modelling. Their operational semantics come in two main
flavours: geometric (in terms of posets, graphs, and such), and
algebraic (in terms of monoids, monoidal categories, etc.). People
have struggled for many years to reconcile the two viewpoints, the
problem being an issue with symmetries. In this talk I will explain
how the problem can be overcome with the help of some elementary
homotopy viewpoints. The new formalism for Petri nets is based on
polynomial-style finite-set configurations and etale maps. The
processes of a Petri net P are etale maps G -> P from graphs. The
main result I want to arrive at is that P-processes (the geometric
semantics) form a symmetric monoidal Segal space, and that this
is the free prop-in-groupoids on P (thus at the same time the
algebraic semantics). But most of the time will be spent just
explaining Petri nets, markings, firings, and the token game.

Reference: "Elements of Petri nets and processes" [ArXiv:2005.05108]