# Application and Theory of Petri Nets: 33rd International - download pdf or read online

By Tony Hoare (auth.), Serge Haddad, Lucia Pomello (eds.)

ISBN-10: 3642311318

ISBN-13: 9783642311314

This booklet constitutes the refereed court cases of the thirty third overseas convention on functions and conception of Petri Nets and Concurrency, PETRI NETS 2012, held in Hamburg, Germany, in June 2012. The 18 usual papers and three software papers offered have been rigorously reviewed and chosen from fifty five submissions. The publication additionally comprises 2 invited talks. All present concerns on learn and improvement within the zone of Petri nets and comparable types of concurrent platforms are addressed.

**Read or Download Application and Theory of Petri Nets: 33rd International Conference, PETRI NETS 2012, Hamburg, Germany, June 25-29, 2012. Proceedings PDF**

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**Extra info for Application and Theory of Petri Nets: 33rd International Conference, PETRI NETS 2012, Hamburg, Germany, June 25-29, 2012. Proceedings**

**Example text**

Halager, and M. Westergaard We construct the model by ﬁrst constructing the state space of the ﬁrst epoch, where the populations are H, C and G. g. H, so tokens are mapped (p, (l, r)) → (H, (l, r)) whenever p is H or C. For the second epoch, we compute the state space of all states reachable from these mapped states (but not states from the ﬁrst epoch where tokens can be in population C). For the third epoch we repeat this, but now mapping G populations to H as well. When computing the probability of paths in the system, we add this projection of states as well.

So CloverS terminates on at least all inputs where the generalized Karp-Miller tree procedure terminates. We can say more: Proposition 6. The procedure CloverS terminates on strictly more input states s0 ∈ S than the generalized Karp-Miller tree procedure. Proof. Consider the reset Petri net of [DFS98, Example 3] again (Figure 3). Add a new transition t5 (n1 , n2 , n3 , n4 ) = (n1 + 1, n2 + 1, n3 + 1, n4 + 1). 1. On the other hand, by fairness, CloverS will sooner or later decide to pick a pair of the form (t5 , a) at line (a), and then immediately terminate with the maximal state (ω, ω, ω, ω), which is the sole element of the clover.

We deduce the following strong relationship between well-structured ACS and complete well-structured ACS. Theorem 10. The completion of an ACS S is an ∞-eﬀective complete WSTS iﬀ S is a strongly monotonic WSTS. Proof. Strong monotonicity reduces to partial monotonicity of each map f , as discussed above. Well-structured ACS are clearly eﬀective, since P ost(s) = {t | ∃f ∈ F · f (t) = s} is Presburger-deﬁnable. Note also that monotonic aﬃne function are continuous, and Nnω is a continuous dcwo. Finally, for every Presburger monotonic aﬃne function f , the function f ∞ is recursive, so the considered ACS is ∞-eﬀective.

### Application and Theory of Petri Nets: 33rd International Conference, PETRI NETS 2012, Hamburg, Germany, June 25-29, 2012. Proceedings by Tony Hoare (auth.), Serge Haddad, Lucia Pomello (eds.)

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