By Fabrice Kordon, Daniel Moldt

ISBN-10: 3319390856

ISBN-13: 9783319390857

ISBN-10: 3319390864

ISBN-13: 9783319390864

This e-book constitutes the lawsuits of the thirty seventh overseas convention on program and thought of Petri Nets and Concurrency, PETRI NETS 2016, held in Toruń, Poland, in June 2016. Petri Nets 2016 used to be co-located with the appliance of Concurrency to process layout convention, ACSD 2016.

The sixteen papers together with three software papers with four invited talks offered jointly during this quantity have been rigorously reviewed and chosen from forty two submissions.

Papers providing unique learn on software or conception of Petri nets, in addition to contributions addressing subject matters appropriate to the final box of disbursed and concurrent structures are offered inside of this quantity.

**Read Online or Download Application and Theory of Petri Nets and Concurrency: 37th International Conference, PETRI NETS 2016, Toruń, Poland, June 19-24, 2016. Proceedings PDF**

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**Extra resources for Application and Theory of Petri Nets and Concurrency: 37th International Conference, PETRI NETS 2016, Toruń, Poland, June 19-24, 2016. Proceedings**

**Example text**

A word w ∈ T ∗ is called a subword (or factor) of w ∈ T ∗ if ∃u1 , u2 ∈ T ∗ : w = u1 w u2 . A word w = t1 t2 . . tn of length n ∈ N uniquely corresponds to a ﬁnite transition system T S(w) = ({0, . . , n}, {(i − 1, ti , i) | 0 < i ≤ n ∧ ti ∈ T }, T, 0). Characterising Petri Net Solvable Binary Words 41 An initially marked Petri net is denoted as N = (P, T, F, M0 ) where P is a ﬁnite set of places, T is a ﬁnite set of transitions with P ∩ T = ∅, F is the ﬂow function F : ((P × T ) ∪ (T × P )) → N specifying the arc weights, and M0 is the initial marking (where a marking is a mapping M : P → N, indicating the number of tokens in each place).

Let w ∈ {a, b}∗ be a solvable word, decomposable into w = an bα with n ≥ 1 and α ∈ {a, b}∗ . Then, bα does not contain the factor aa or it does not contain the factor bb. Proof: Assume w contains both factors aa and bb in bα. Select “neighboring” factors aa and bb, such there is no other factor aa or bb in between. Since neither chosen factor is at the start of the word, w can be decomposed into w = βabi bb(ab)j aaγ or w = βbai aa(ba)j bbγ with β, γ ∈ {a, b}∗ and i, j ≥ 0. The neighbors aa and bb have been underlined.

We do not know whether the converse holds, and thus the following question is open: Question 1. For every homogeneous A such that (Age(A), ✂) is a wqo, and for every wqo (X, ≤), is the lifted quasi-order (Age(A, X), ✂(X,≤) ) a wqo? Let’s concentrate on an important special case, when (X, ≤) = (Age(B), ✂) for some homogeneous structure B. We observe that Age(A, Age(B)), containing induced substructures of A labeled by induced substructures of B, is essentially the same set as Age(A ⊗ B), containing induced substructures of the wreath product.

### Application and Theory of Petri Nets and Concurrency: 37th International Conference, PETRI NETS 2016, Toruń, Poland, June 19-24, 2016. Proceedings by Fabrice Kordon, Daniel Moldt

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