<p>Found another article that helped me understand:</p>

<p>COMPEXITY OF SOME PROBLEMS IN PETRI NETS* </p>

<p><a href="http://www.sciencedirect.com/science/article/pii/0304397577900147" rel="nofollow noreferrer">http://www.sciencedirect.com/science/article/pii/0304397577900147</a></p>

<p>This paper does a good job of explaining the difference between a k-bounded Petri-Net and an unbounded one.</p>

<p>A Petri net is bounded if and only if it has a finite reachability set. </p>

<p>Bouziane’s solution applies only to bounded Petri-Nets. </p>

CC BY-SA 3.0
2017-11-20T14:12:39.353Z
2017-11-20T14:12:39.353Z
stackdump
<p>This paper seems to point out that Bouziane’s solution is incorrect.</p>

<p><a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.143.9009&amp;rep=rep1&amp;type=pdf" rel="nofollow noreferrer">http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.143.9009&amp;rep=rep1&amp;type=pdf</a></p>

<p>In the conclusion: </p>

<blockquote>
  <p>This false claim served for deriving a bound on the number of states
  of the constructed automaton – which in reality can have infinitely
  many states.</p>
</blockquote>

<p>I think I understand this point as it relates to the general reachibility problem, However The Petri-Net used as an illustration contains 'loops' at transitions: t3 and t1 - transitions that have both incoming and outgoing arcs.</p>

<p>If Petri-Net being examined were composed of only elementary paths, the resulting witness sequence / state machine language would not be susceptible to the pumping lemma.</p>

<p>Does this seem accurate? why or why not?</p>

<petri-nets>
Bouziane’s transformation of the Petri net reachability problem and incorrectness
stackdump
# Bouziane’s transformation of the Petri net reachability problem and incorrectness

(Asked by: username_0 on 2017-11-14)

This paper seems to point out that Bouziane’s solution is incorrect.

<http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.143.9009&rep=rep1&type=pdf>

In the conclusion:

> This false claim served for deriving a bound on the number of states
> of the constructed automaton – which in reality can have infinitely
> many states.

I think I understand this point as it relates to the general reachibility problem, However The Petri-Net used as an illustration contains 'loops' at transitions: t3 and t1 - transitions that have both incoming and outgoing arcs.

If Petri-Net being examined were composed of only elementary paths, the resulting witness sequence / state machine language would not be susceptible to the pumping lemma.

Does this seem accurate? why or why not?

**Tags:** petri-nets

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## 1 answers

### Answer by username_0 on 2017-11-20. Score: 1

Found another article that helped me understand:

COMPEXITY OF SOME PROBLEMS IN PETRI NETS\*

<http://www.sciencedirect.com/science/article/pii/0304397577900147>

This paper does a good job of explaining the difference between a k-bounded Petri-Net and an unbounded one.

A Petri net is bounded if and only if it has a finite reachability set.

Bouziane’s solution applies only to bounded Petri-Nets.


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