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Proof that flows form a prefix order

In this module/week, you will be really training your abstract thinking skills. After finishing this module, you will have learned how to formalize the behavior of any dynamical system as a prefix order, and how to formalize the interpretation of a consumption/production system as a counting function on such a prefix order. You understand how the Petri-net interpretation puts certain restrictions on these counting functions, and how you can exploit those restrictions to prove properties about Petri-net interpretations, without knowing the actual interpretation itself. At the end of the module, you will practice the formalization of performance metrics as logical properties of counting functions, by recognizing right and wrong examples of formalization. Those who are already familiar with Petri-net theory, may find that the prefix order semantics that I introduce in this course is slightly different from what they are used to. Traditional Petri-net semantics is usually based on markings, transition systems, or the execution trees thereoff. Execution trees are a particular example of a prefix order, but in general prefix orders offer the added flexibility that they do not restrict the user to discrete interpretations of behavior only. This is particularly suitable when seeking connection between theoretical computer science and an application field like embedded systems, from which this course originates, where also the continuous behavior of physical systems has to be taken into account.

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