Download PDFOpen PDF in browser

A Survey of Elementary Object Systems

18 pagesPublished: May 15, 2012


This contribution presents the formalism of ElementaryObjectSystems (Eos). Object nets are Petri nets which have Petri nets as tokens – an approach known as the nets-within-nets paradigm. One central aim of this contribution is to compile all our previous works ded- icated to certain aspects of Eos together with recent yet unpublished results within one self-contained presentation. Since object nets in general are immediately Turing complete, we introduce the restricted class of elementary object nets which restrict the nesting of nets to the depth of two. In this work we study the relationship of Eos to existing Petri net formalisms. It turns out that Eos are more powerful than classical p/t nets which is demonstrated by the fact that e.g. reachability and liveness become undecidable problems for Eos. Despite these undecidability results other properties can be extended to Eos using a monotonicity argument similar to that for p/t nets. Also linear algebraic techniques, especially the theory of linear invariants and semiflows, can be extended in an appropriate way. The invariant calculus for Eos even enjoys the property of compositionality, i.e. invariants of the whole system can be composed of invariants of the object nets, which reduces the computational effort. To obtain a finer level of insight we also studied several classes like pure, minimal, or semi-bounded Eos. Among these variants the subclass of generalised state machines is worth mentioning since it combines the decidability of many theoretically interesting properties with a quite rich practical modelling expressiveness.

Keyphrases: decidability questions, Mobility, nets-within-nets, object nets, Petri nets

In: Berndt Müller (editor). LAM'10. 3rd International Workshop on Logics, Agents, and Mobility, vol 7, pages 19--36

BibTeX entry
  author    = {Michael K\textbackslash{}"ohler-Bu\{\textbackslash{}ss\}meier},
  title     = {A Survey of Elementary Object Systems},
  booktitle = {LAM'10. 3rd International Workshop on Logics, Agents, and Mobility},
  editor    = {Berndt M\textbackslash{}"uller},
  series    = {EPiC Series in Computing},
  volume    = {7},
  pages     = {19--36},
  year      = {2012},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/dqbd}}
Download PDFOpen PDF in browser