Accept/Reject the following statements by providing a brief argument for/against each. Draw an example, if applicable,...

Accept/Reject the following statements by providing a brief argument for/against each. Draw an example, if applicable, that supports your argument. (A simple true/false answer will not earn you any points. I am also not looking for formal proofs.)

a. A Place-Transition net system with infinite reachability set will also be unbounded

b. A Petri net system will be reversible if all states in its reachability set are home states

c. An unbounded PN system will also be deadlock free.

Solutions

Expert Solution

a. A Place-Transition net system with infinite reachability set will also be unbounded

Answer : The above statement stated is true, as the infinite reachability set will also be unbounded.

It may consist of a correspinding graph that is infinitely large and the number of tokens in a tree is basically unbounded which may grow to any number by just executing the cycles in a transition and tokens.

eg . Below given the diagram explains that t1, t2, t2 are set of transitions and p1, p2, p3 are set of places. Here the number of tokens will increase between T1 and T2, hence resulting into different number of tokens for p3, thus its is unbounded.

b. A Petri net system will be reversible if all states in its reachability set are home states

Answer: The above stated answer is true, as a petri net is said to be reversible if the initial markings remains reachable from any reachable marking.

A markings is said to be a home state if it is reachable from all the reachable markings and also existence of home state is important for systemsrequiring a proper termination point.

Note : Reversibility implies existence of home states but the reverse is not true.

c. An unbounded PN system will also be deadlock free.

Answer : A petri net is said to be deadlock free if it does not contain any deadlock.

The petri net will always have a deadlock independant of the initial marking and also a petri net will be deeadlock free if each reachable marking enables minimum one transition in it.

venereology answered 4 months ago

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