Enabled Transition and Transition Firing Assignment Help

Basic Introduction To PETRI NETS - Enabled Transition and Transition Firing

Definition 5: Enabled Transition and Transition Firing

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

M (pi) ≥ IN ( pi,tj ) ∀ pi ∈ IP (tj )

Furthermore if a transition is as to be enabled such it can fire freely at any time. At this time, if any enabled transition tj 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 tj generates a marking M′ from earlier marking M. Hence we have,

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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 Mj is reach-able also from Mi and Mk is reach-able from Mj then the marking Mk is reachable from Mi. Hence we have that on a set of markings, transitive and reflexive relations hold good for the reach-ability of markings.

 


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