Modeling with TS will produce extremely complex graph

In contrast to state machines, state transitions in Petri nets are asynchronous. The ordering of transitions is partly uncoordinated; it is specified by a partial order.

Therefore, Petri nets can be used to model concurrent distributed systems.

• Two kinds of node:
  • Place: resources or partial state of the system
  • Transitions: state transition and synchronization
• Arcs are directed and always connect nodes of different types
• Tokens are resources in the places

Formalism

$$ C = (P,T,I,O) $$

where:

• Place $P = \{p_1,p_2,…,p_n\}$
• Transitions $T = \{t_1,t_2,…,t_n\}$
• Input $\cdot t$
• Output $t \cdot$

Marking $\mu$: assignment of tokens to the places of Petri net

$\mu = \mu_1, \mu_2,…,\mu_n$

Transitions