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On the Complexity of the Reachability Problem for Safe : Elementary Hornets

Köhler-Bußmeier M.

Fundamenta Informaticae

2014

Vol. 129, nr 1/2

101--115

In this paper we study the complexity of HORNETS, an algebraic extension of object nets. We define a restricted class: safe, elementary HORNETS, to guarantee finite state spaces. It will turn out, that the reachability problem for this class requires exponential space, which is a major increase when compared to safe, elementary object nets, which require polynomial space.

A Survey of Decidability Results for Elementary Object Systems

Köhler-Bußmeier M.

Fundamenta Informaticae

2014

Vol. 130, nr 1

99--123

This contribution presents recent results on Elementary Object Systems (EOS). Object nets are Petri nets which have Petri nets as tokens – an approach known as the nets-within-nets paradigm. In this work we study the relationship of EOS to existing Petri net formalisms. It turns out that EOS are equivalent to counter programs. But even for the restricted subclass of conservative EOS reachability and liveness are undecidable problems. On the other hand for other properties like boundedness are still decidable for conservative EOS. We also study the sub-class of generalised state machines, which is worth mentioning since it combines decidability of many theoretically interesting properties with a quite rich practical modelling expressiveness.

The Reachability Problem for Object Nets

Köhler M.

Fundamenta Informaticae

2007

Vol. 79, nr 3-4

401-413

In this article I will prove undecidability results for elementary object net systems ( EOS). Object nets are Petri nets which have Petri nets as tokens - an approach which is called the "nets-within-nets" paradigm. EOS are special object net systems which have a two leveled structure.