Applications and Theory of Petri Nets: 30th International by Joseph Sifakis (auth.), Giuliana Franceschinis, Karsten Wolf

By Joseph Sifakis (auth.), Giuliana Franceschinis, Karsten Wolf (eds.)

This booklet constitutes the refereed court cases of the thirtieth foreign convention on purposes and concept of Petri Nets and different versions of Concurrency, PETRI NETS 2009, held in Paris, France, in June 2009.

The 19 revised papers categorised as thought papers (13), software papers (1), and power papers (5) have been conscientiously reviewed and chosen from forty six submissions. All present matters on examine and improvement within the region of Petri nets and similar versions of concurrent platforms are addressed, novel instruments in addition to monstrous improvements to current instruments are presented.

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Additional resources for Applications and Theory of Petri Nets: 30th International Conference, PETRI NETS 2009, Paris, France, June 22-26, 2009. Proceedings

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Tn , σ2 = t1 . . ti−1 ti+1 ti ti+2 . . tn be occurrence sequences of P N . Then σ1 ≡0 σ2 iff σ = {t1 } . . {ti−1 }{ti , ti+1 }{ti+2 } . . {tn } is a step sequence of P N . It is easy to see that ≡0 is symmetric and therefore ≡∗0 is an equivalence relation. Definition 27 (Exchange Equivalence). The equivalence relation ≡∗0 on occurrence sequences of P N is called exchange equivalence. Based on the results in [10] we state that the extension equivalence restricted to OL(P N ) and exchange equivalence coincide: Theorem 8.

It is easy to see that ≡0 is symmetric and therefore ≡∗0 is an equivalence relation. Definition 27 (Exchange Equivalence). The equivalence relation ≡∗0 on occurrence sequences of P N is called exchange equivalence. Based on the results in [10] we state that the extension equivalence restricted to OL(P N ) and exchange equivalence coincide: Theorem 8. For each lto1 , lto2 ∈ OL(P N ) : lto1 ≡∗0 lto2 ⇔ lto1 ≡ lto2 . 4 Results and Related Works As we mentioned in Introduction, motivation for introducing token flows was to have not only a unifying framework for different flavours of Petri net semantics, but to have also a simple formalism and effective technique to solve problems.

Its central arguments are outlined in the Appendix. 6 Examples Revisited Turning back to the composition of nets in Sec. 2, we just have to indicate the ports of the involved nets. Composition then follows Definition 10. The ports L and R of the run snippets r1 , r2 , r3 in Fig. 2 are obvious: L contains the places p with empty pre-set . p, and R the places p with empty post-set p. This convention makes r1 , r2 and r3 interface nets, with compositions as shown in Fig. 3. Matters are more involved for r1 in Fig.

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