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Timed Basic Parallel Processes

Authors Lorenzo Clemente , Piotr Hofman , Patrick Totzke

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Author Details

Lorenzo Clemente
  • University of Warsaw, Poland
Piotr Hofman
  • University of Warsaw, Poland
Patrick Totzke
  • University of Liverpool, UK

Funding

  • Clemente, Lorenzo: Partially supported by Polish NCN grant 2017/26/D/ST6/00201.
  • Hofman, Piotr: Partially supported by Polish NCN grant 2016/21/D/ST6/01368.

Acknowledgements

Many thanks to Rasmus Ibsen-Jensen for helpful discussions and pointing us towards [Hansen et al., 2013].

Cite As Get BibTex

Lorenzo Clemente, Piotr Hofman, and Patrick Totzke. Timed Basic Parallel Processes. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.CONCUR.2019.15

Abstract

Timed basic parallel processes (TBPP) extend communication-free Petri nets (aka. BPP or commutative context-free grammars) by a global notion of time. TBPP can be seen as an extension of timed automata (TA) with context-free branching rules, and as such may be used to model networks of independent timed automata with process creation. We show that the coverability and reachability problems (with unary encoded target multiplicities) are PSPACE-complete and EXPTIME-complete, respectively. For the special case of 1-clock TBPP, both are NP-complete and hence not more complex than for untimed BPP. This contrasts with known super-Ackermannian-completeness and undecidability results for general timed Petri nets. As a result of independent interest, and basis for our NP upper bounds, we show that the reachability relation of 1-clock TA can be expressed by a formula of polynomial size in the existential fragment of linear arithmetic, which improves on recent results from the literature.

Subject Classification

ACM Subject Classification
  • Theory of computation → Timed and hybrid models
Keywords
  • Timed Automata
  • Petri Nets

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