Petri Nets

@article{Peterson1977PetriN,
  title={Petri Nets},
  author={James L. Peterson},
  journal={ACM Comput. Surv.},
  year={1977},
  volume={9},
  pages={223-252}
}
Over the last decade, the Petr i net has gamed increased usage and acceptance as a basic model of systems of asynchronous concurrent computation. This paper surveys the basic concepts and uses of Petm nets. The structure of Petr i nets, thei r markings and execution, several examples of Petm net models of computer hardware and software, and research into the analysis of Petm nets are presented, as are the use of the reachabil i ty tree and the decidability and complexity of some Petr i net… 
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  • 2019
TLDR
This article presents an extension of Petri nets, in which places can be grouped into so-called “units” expressing sequential components, which can be recursively nested to reflect both the concurrent and hierarchical nature of complex systems.
Tyne An Algebra of Timed-Arc Petri Nets
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Performance Evaluation of Asynchronous Concurrent Systems Using Petri Nets
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An extended timed Petri net model is used to model clearly the synchronization involved in these systems, and it is found that the computational complexity involved increases in the same order as they are listed above.
Petri Nets: Properties, Analysis and Appl ka t ions
This is an invited tutorial-review paper on Petri nets-a graphical and mathematical modeling tool. Petri nets are a promising tool for describing and studying information processing systems that are
On the Problem of Characterizing Boolean Petri Nets
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The aim of this paper is to present some basic results and necessary and sufficient condition for a 1-safe Petri net that generates all the binary nvectors as marking vectors, and shall call such Petrinets as Boolean Petri nets.
Distributing Finite Automata Through Petri Net Synthesis
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It is shown that the general Petri net synthesis problem and its distributed version may both be solved in time polynomial in the size of the given graph.
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References

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Petri Nets and Szilard Languages
TLDR
After introducing new normal forms for Petri nets, it is proved that the reachability problem is equivalent to the emptiness problem for the intersection of Szilard languages and the methodology presented should also apply to related models for representing parallel processes such as Karp and Miller and Gostelow.
Comments on capabilities, limitations and “correctness” of Petri nets
TLDR
The capabilities and limitations of Petri nets are examined and techniques for proving their correctness are investigated and the feasibility of using the methods of computational induction and inductive assertions to prove restricted statements about Petrinets is established.
Comments on capabilities, limitations and “correctness” of Petri nets
TLDR
The capabilities and limitations of Petri nets are examined and techniques for proving their correctness are investigated and the feasibility of using the methods of computational induction and inductive assertions to prove restricted statements about Petrinets is established.
ANALYSIS OF PRODUCTION SCHEMATA BY PETRI NETS
TLDR
This thesis presents results on structural constraints guaranteeing global operation, and decompositions of complex systems into meaningful parts, and for a corresponding class of systems called Production Schemata.
ANALYSIS OF ASYNCHRONOUS CONCURRENT SYSTEMS BY TIMED PETRI NETS
This thesis is concerned with the modeling and performance analysis of systems which consist of concurrently acting components, an example of which is an asynchronous pipelined processor. The work is
Macro E-Nets for Representation of Parallel Systems
TLDR
Previous work on evaluation nets is extended through the use of macro nets that represent structures made up of the primitives, allowing compression of the net for easier understanding.
Decidability Questions for Petri Nets
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  • Mathematics, Computer Science
    Outstanding Dissertations in the Computer Sciences
  • 1975
TLDR
A number of Petri Net problems are shown to be recursively equivalent to the Reachability Problem for Vector Addition Systems, and the equality of Reachability Sets and the equivalence of two Petri Nets in terms of their language-generating capability are recursive undecidable.
A Comparison of Some Theoretical Models of Parallel Computation
TLDR
This paper describes and compares a number of theoretical models for parallel computation; namely, Petri nets, computation graphs, and parallel program schemata, and shows how marked graphs, a particular type of Petri net, are a restricted type of computation graph.
Computation Sequence Sets
TLDR
A class of automata based upon generalized Petri nets is introduced and defined, and the class of CSS languages is shown to be closed under union, intersection, concatenation, and concurrency.
Termination Properties of Generalized Petri Nets
  • Y. E. Lien
  • Mathematics, Computer Science
    SIAM J. Comput.
  • 1976
TLDR
A generalization of Petri nets and vector addition systems, called GPN and MGPN, is introduced and the main results obtained are every strongly connected, strongly repetitive and forward- (or backward-) conflict-free GPN must be conservative.
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