add petri nets

slides/pages/recap.md

@@ -28,3 +28,106 @@ title: Recap I
 
 </v-clicks>
 
+---
+title: Recap II
+layout: two-cols
+---
+
+### Petri Nets
+
+Petri Nets is one of the modeling languages for modeling systems with **concurrency and resource sharing**; developed in 60s by [Carl Adam Petri](https://www.wikiwand.com/en/Carl_Adam_Petri).
+
+Further information: [link](https://www2.informatik.uni-hamburg.de/TGI/PetriNets/index.php)
+
+#### Tools
+
+- [TikZ](https://latexdraw.com/petri-nets-tikz/) allows you to draw Petri Nets in Latex
+- [Snoopy](https://www-dssz.informatik.tu-cottbus.de/DSSZ/Software/Snoopy) is software tool to design and animate hierarchical graphs, among others Petri Nets. (Available on MacOS, Windows, Linux)
+
+::right::
+
+#### Overview
+
+The standard notion of Petri nets (PN) does not involve any timing aspects. Those nets are purely qualitative, i.e. time-free models.
+
+<div class="container flex justify-center mt-10">
+    <img src="/images/Petri-Nets-types.png" class="block w-lg"/>
+</div>
+
+---
+title: Recap III
+---
+
+### Basics
+
+Standard Petri Nets consist of places, transitions, arcs and tokens:
+
+- Only places are allowed to carry tokens 
+- Two nodes of the same type can not be connected with each other
+- A transition is enabled and may fire if its pre-places are sufficiently marked by tokens.
+
+<div class="container flex justify-center mt-10">
+    <img src="/images/Petri-Nets-basics.png" class="block w-3/4"/>
+</div>
+
+
+---
+title: Recap IV
+---
+
+### Typical Structures
+
+<div class="container flex justify-center">
+    <img src="/images/Petri-Nets-structures.png" class="block w-3/4"/>
+</div>
+
+
+---
+title: Recap V
+---
+
+### Exercises
+
+<br/>
+
+#### Modeling an Elevator
+
+The elevator moves between four floors and can stop at any of these floors. The elevator can either go up or go down.
+
+#### Modeling X-ray Examination in the Hospital
+
+A hospital has one X-ray department. If a patient wants to do a X-ray examination, it has to go through the following stages:
+
+- The patient waits outside the room.
+- The patient enters the room after the last patient is gone.
+- The patient takes the X-ray photo.
+- The patient leaves the room.
+
+It's very important to the X-ray department, that only one patient can enter the room and take the photo at a time.
+
+
+---
+title: Recap VI
+---
+
+#### Advantages of Petri Nets (Standard)
+
+<v-clicks>
+
+- Mathematical foundation (1-1 correspondence between mathematical notation and graphical representation)
+- Simple graphical notation
+- Does not explicitly represent the state space of a process (compact and ignores irrelevant details)
+
+</v-clicks>
+
+<br/>
+
+#### Limitations of Petri Nets (Standard)
+
+<v-clicks>
+
+- Large network size (tendency to become very large)
+- Limited expressive power (how to model something like $x \leq y$ when $x$ and $y$ are unknown at design time?)
+- No explicit modeling of time. (hard to indicate _when_ and _how long_)
+
+</v-clicks>