Petri Nets for Systems Engineering: A Guide to Modeling, by Claude Girault

By Claude Girault

Utilizing formal tools for the specification and verification of and software program structures is turning into more and more very important as platforms elevate in measurement and complexity. the purpose of the publication is to demonstrate growth in formal equipment in accordance with Petri web formalisms. It provides either functional and theoretical foundations for using Petri nets in advanced procedure engineering initiatives. In doing so it bridges the space among Petri nets and the platforms modeling and implementation strategy. It incorporates a number of examples coming up from assorted fields, similar to versatile production, telecommunication and workflow administration platforms.

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Additional resources for Petri Nets for Systems Engineering: A Guide to Modeling, Verification, and Applications

Example text

Not every abstraction, however, has a meaningful interpretation. 13a. 13d has a corresponding behaviour ("a token is passed through"). 13b, but now the behaviour is different. 13b. Note that the set Y to be abstracted is not necessarily connected as a subgraph. 13d can be interpreted as a merge of two places. This operation is called a fusion of places or place fusion. It will be used in Part II of this book to create larger nets from smaller ones. 13c. 13e-h. 13f, g and h describe a fusion of transitions or transition fusion.

Therefore the colour domain mapping cd is extended from P to PUT. In the entries of the incidence matrices for each transition colour, a multiset has to be specified. This is formalised by a mapping from cd(t) into the bags of colour sets over cd(p) for each (p, t) E P x T. 1. A coloured Petri net (CPN) is defined by a tuple N = (P, T, Pre, Post, C, cd), where • • • • • P is a finite set (the set of places of N), T is a finite set (the set of transitions of N), disjoint from P, C is the set of colour classes, cd: PUT -+ C is the colour domain mapping, and Pre, Post E BIPI x ITI are matrices (the backward and forward incidence matrices ofN) such that Pre[p,t]: cd(t) -+ Bag(cd(p)) and Post[p,t]: cd (t) -+ Bag( cd (p)) are mappings for each pair (p, t) E P x T.

If in b) a binding such as (32 = [x = a,Y = b,z = c] is selected, then the transition is not activated in this binding (or mode) since the guard is not satisfied. For a binding such as (33 = [x = b, Y = b, z = b] the guard holds, but there are insufficient tokens in the input places, namely there are not two copies of b in Pl. The selection of a binding is local to a transition. Hence, the variable z in N5 can be replaced by x without changing the behaviour of the net. Applying the occurrence rule to the CPN N 5 , we obtain the same behaviour as for N 4 .

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