Addressing the Schema Representation Problem in Process Models Using Petri Nets—First Results Illustrated by the Dining Philosophers Problem

In this paper, we introduce the schema representation problem using the example of dining philosophers: The difference between a system model of five eating philosophers and a schema model for a set of eating philosophers is of major importance. In a Petri net model, each philosopher and each fork would be considered as separate entities with their relating states and transitions. However, this approach lacks due to scalability and dynamic behavior, as adding more philosophers and forks significantly increases the model’s size. To model any set of dining philosophers, a Petri net schema is useful. However, there is no modeling technique to model an infinite set of philosophers and forks, and to access its single elements. To address this problem, we provide the elm-notation, which allows us to dynamically unfold and aggregate any sets whereby behavior can be described for each philosopher and fork on schema level.