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#+TITLE: Petri Nets for Biomodelling: An Introduction

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The goal of this course is to introduce students to [[https://en.wikipedia.org/wiki/Petri_net][Petri nets]],
explore some of their properties, and show how Petri nets can be used
in biomodelling. After having taken this course, the students will be
able to build Petri net models of biological phenomena (including
using some extensions, like basic coloured Petri nets and inhibitors
arcs) and to relate the formal properties of these models to the
biological properties of the modelled phenomenon.

This course does not require prior experience in theoretical computer
science or biology and is part of the course "Network medicine" taught
to students following the [[https://www.universite-paris-saclay.fr/fr/education/master/m2-genomics-informatics-and-mathematics-for-health-and-environment-geniomhe#presentation-m2][GENIOMHE]] MSc. program at [[http://www.univ-evry.fr/fr/index.html][Université
d'Évry]].

The course consists of 4 sections, the first three focusing on Petri
nets and their properties and the last one being a practical
assignment. The sections are designed to reflect logical differences
in content and need not correspond to actual sessions.

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The materials of this course are distributed under the [[https://en.wikipedia.org/wiki/Creative_Commons_license][Creative
Commons Attribution Alone licence]].


* Definitions
  This section starts by motivating the model of Petri nets and gives
  the definition of the model and of the evolution modes. Particular
  focus is on the synchronous and the asynchronous evolution
  modes. The parallel with [[https://en.wikipedia.org/wiki/Multiset][multiset]] rewriting is also shown.

  The slides for this section are available [[file:../content/courses/pn-biomodelling/network-medicine-4.pdf][here]].

* Extensions
  This sections briefly points some limitations of the original Petri
  net model and shows the classical extended variants, like coloured
  tokens or inhibitor arcs. The cost of extensions is intuitively
  evaluated with respect to decidability: more expressive variants are
  often undecidable.

  The slides for this section are available [[file:../content/courses/pn-biomodelling/network-medicine-5.pdf][here]].

* Properties
  In this section some of the fundamental structural and behavioural
  properties of Petri nets are presented. Behavioural properties are
  introduced before structural properties because the former are
  easier to grasp. This section includes a number of exercises to be
  done interactively with the students. Additional exercises may be
  given on the whiteboard.

  The slides for this section are available [[file:../content/courses/pn-biomodelling/network-medicine-6.pdf][here]].

* Case Studies
  This section is a practical assignment in which the students should
  use Petri nets to model and analyse two simplified biological
  networks. [[http://projects.laas.fr/tina/][The TINA toolbox]] is the suggested tool for Petri net
  analysis, even though other tools may also be used.

  The text of this assignment is [[file:../content/courses/pn-biomodelling/network-medicine-pn.pdf][here]].


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