Sergiu Ivanov

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===== Petri Nets for Biomodelling: An Introduction =====

The goal of this course is to introduce students to 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.

The materials of this course are distributed under the [[https://en.wikipedia.org/wiki/Creative_Commons_license|Creative Commons Attribution Alone licence]] {{:ccby.png?60}}

==== 1. 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 multiset rewriting is also shown.

The slides for this section are available {{:network-medicine-4.pdf|here}}.

==== 2. 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 {{:network-medicine-5.pdf|here}}.

==== 3. 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 {{:network-medicine-6.pdf|here}}.

==== 4. 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 {{:network-medicine-pn.pdf|here}}.
Sergiu Ivanov

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