Petri Net Model for Serious Games Based on Motivation Behavior Classification

Table 3

Formal definition of a Petri net.

A Petri net is a 5 tuple, PN = (P, T, F, W, 𝑀0) where
P = {𝑝1,𝑝2,…,𝑝𝑚} is a finite set of places,
T = {𝑡1,𝑡2,…,𝑡𝑛} is a finite set of transitions,
𝐹⊆(𝑃×𝑇)∪(𝑇×𝑃) is a set of arcs (flow relation),
𝑊∶𝐹→{1,2,3,…} is weight function,
𝑀0∶𝑃→{0,1,2,3,…} is the initial marking,
𝑃∩𝑇=∅ and 𝑃∪𝑇≠∅.
A Petri net structure 𝑁=(𝑃,𝑇,𝐹,𝑊) without any specific initial; marking is denoted by 𝑁.
A Petri net with the given initial marking is denoted by (𝑁,𝑀0).