Reversible or Proper Petri Net
If the initial marking is reach-able from each reach-able marking well in either one or more steps then the Petri net is termed as a Proper Petri net.
If the system fails at sometime, the property of properness inside a Petri net ensures about the system can be reinitialized automatically from such state. Hence the property of properness is often submitted to as reinitialize-ability or reversibility of the system. Mathematically we have,
M0 ∈ R [M] ∀M ∈ R [M0]