Applications and Theory of Petri Nets: 29th International by Gustavo Alonso (auth.), Kees M. van Hee, Rüdiger Valk (eds.)

By Gustavo Alonso (auth.), Kees M. van Hee, Rüdiger Valk (eds.)

This ebook constitutes the refereed lawsuits of the twenty ninth foreign convention on purposes and conception of Petri Nets and different types of Concurrency, PETRI NETS 2008, held in Xi'an, China, in June 2008.

The 19 revised complete commonplace papers and four revised instrument papers provided including five invited papers have been rigorously reviewed and chosen from seventy five submissions. All present concerns on learn and improvement within the zone of Petri nets and modeling of concurrent structures are addressed.

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Example text

Equals the marking reached after σ(τ − As the above (Keller’s) theorem is the basis for our subsequent results, we include a proof of this theorem in the Appendix. In the end of the present section, we establish a series of consequences of Theorem 1. Corollary 1. Directedness of persistent nets Let N be a persistent net and let M1 and M2 be two reachable markings. Then there is some marking M3 which is reachable from M1 and from M2 . Proof: By the definition of reachability, there are two sequences τ and σ leading from the initial marking M0 to M1 and to M2 , respectively.

Darondeau net is semilinear, and Grabowski’s proof of the decidability of persistence of vector addition systems [6]. Since then, however, some new open questions have arisen in this context. It is the purpose of this paper to go some way towards solving such questions and, more generally, to help making structure theory more amenable to persistent nets. In particular, we show that for bounded and reversible persistent nets, a decomposition of the cycles of the reachability graph (and thus, of the realisable T-invariants) into smaller, disjoint cycles can be found.

3) • • • • • Because a is not contained in τ − σ, we have ((τ − σ)− a) = (τ − σ). Hence, τ − σ is • • firable from M . Moreover, because τ −σ reproduces M , Ψ (τ −σ) is a T-invariant, and the second part of Equation (3) yields • M [τ − σ M . (4) By Equation (4) and M [τ M (cf. Figure 3), and by Keller’s theorem, • • • M [τ − σ M [τ − (τ − σ) M. (5) The final marking is indeed M , since by Keller’s theorem, it must coincide with • • • • the marking reached by the firing sequence M [τ M [(τ − σ)− τ and (τ − σ)− τ = ε.

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