Nets within Nets

Nets in nets are a modeling approach from the Petri net family.

From other types of Petri nets they stand out by being able to provide brands with an internal structure, which in turn works on Petri net basis. A network can also contain other network copies that will be moved around in it and it can switch itself.

Motivation

Networks in networks are suitable for modeling distributed systems with particular attention to aspects of

  • Hierarchy,
  • Mobility and
  • Encapsulation

In many developments, a strong relation was deliberately sought to object orientation, to model the ability of Petri nets, concurrent processing, to connect to the modeling of objects that can be produced and interact.

History

Based on practical requirements are different formalisms have been developed since the mid- 90s, on the description of the "Networks in Networks' fits. Lomazova and Schnoebelen list in that article some of which are well-known: Sibertin -Blanc, Lakos, Moldt and Wienberg as building on Dyed Petri nets, beside the object of Valk networks.

The earliest use of hierarchical network models can be found at Valk and Jessen, where Valk in a post called " Task / Flow Nets " introduced in order to model application systems compact can. In these models, jobs are running as brands through a network that models its execution; at the same time, the individual orders each having an inner state which stores its history and indicates the extent to which they have already been processed.

Semantics

The main distinction in the interpretation takes place in the treatment of brands. Are brands only references to net specimens that co-exist in a given global state, so it is a reference semantics, brands, however, are to be interpreted even as networks, then there is a value semantics. These differ in the treatment of comparable brands: network brands in the value semantics exist independently and have their own states.

A problem arises not necessarily copying, but no later than during the merge of different copies of the " same " network. Sometimes this is a third type of semantics, which has been suggested in the article that make sense. In this variant of the value semantics, the sequence stories of copies are merged to the smallest flow history, which includes both.

Mixed forms are also possible and sometimes modeling technically relevant.

Communication

Without communication between the network copies can be modeled very little; as in object-oriented programming provide the formalisms therefore usually a communication of objects (network copies) on previously defined interfaces, which are, however, bound dynamically.

Figure 1 shows an example of a network comprising another network. This example is so simple in design that coincide value and reference semantics. The internal network is movable and can be connected as a brand from location "a" to location "b"; the channel addresses appear here as method invocations and ensure that this reflects external condition by the synchronized switching of the " calling " and " called " Transition in the internal network. The "x" at the edges is a variable, which is bound at a transition of the switching network to the external network mark.

Limited formalisms

A major disadvantage of unrestricted formalisms is that some analysis problems (such as the reachability of a given marking) are undecidable. Some of Petri nets known analytical techniques ( such as analysis by linear invariants ), however, remain applicable.

In order to regain decidability, we restrict a possible network structures by making about generating new network copies impossible.

Tools

  • CO - OPN https://smv.unige.ch//research-projects/co-opn based on algebraic Higher networks
  • RENEW http://www.renew.de is a free development environment for reference networks with Java integration

References

  • Theoretical computer science
  • Distributed system
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