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Acceleration For Presburger Petri Nets

3 pagesPublished: July 25, 2013

Abstract

The reachability problem for Petri nets is a central problem of net theory. The problem is known to be decidable by inductive invariants definable in the Presburger arithmetic. When the reachability set is definable in the Presburger arithmetic, the existence of such an inductive invariant is immediate. However, in this case, the computation of a Presburger formula denoting the reachability set is an open problem. Recently this problem got closed by proving that if the reachability set of a Petri net is definable in the Presburger arithmetic, then the Petri net is flatable, i.e. its reachability set can be obtained by runs labeled by words in a bounded language. As a direct consequence, classical algorithms based on acceleration techniques effectively compute a formula in the Presburger arithmetic denoting the reachability set.

Keyphrases: acceleration, Flatability, infinite-state systems, Petri nets, Presburger, reachability, vector addition systems

In: Alexei Lisitsa and Andrei Nemytykh (editors). VPT 2013. First International Workshop on Verification and Program Transformation, vol 16, pages 10--12

Links:
BibTeX entry
@inproceedings{VPT2013:Acceleration_For_Presburger_Petri,
  author    = {Jerome Leroux},
  title     = {Acceleration For Presburger Petri Nets},
  booktitle = {VPT 2013. First International Workshop on Verification and Program Transformation},
  editor    = {Alexei Lisitsa and Andrei Nemytykh},
  series    = {EPiC Series in Computing},
  volume    = {16},
  pages     = {10--12},
  year      = {2013},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/hnX},
  doi       = {10.29007/8wkd}}

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