Definition 5: Enabled Transition and Transition Firing

In a marking M, transition t_j is said to be enabled if,

M (p_i) ≥ IN ( p_i,t_j ) ∀ p_i ∈ IP (t_j )

Furthermore if a transition is as to be enabled such it can fire freely at any time. At this time, if any enabled transition t_j fires, we attain a new marking M′ from the original marking M described by,

M ′ ( pi ) = M ( pi ) + OUT ( pi , t j ) - IN ( pi , t j ) ∀ pi ∈ IP (t j )

Definition 6: Reach-ability

We declare that a marking M′ is reachable from M if firing a transition t_j generates a marking M′ from earlier marking M. Hence we have,

Illustration .7

Prove that reach-ability of a marking is a transitive and reflexive relation on the set of markings.

Solution

We can simply perceive that every marking is trivially reachable from itself with no firing any transition. if a transition M_j is reach-able also from M_i and M_k is reach-able from M_j then the marking M_k is reachable from M_i. Hence we have that on a set of markings, transitive and reflexive relations hold good for the reach-ability of markings.