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Detectability of Labeled Petri Nets

  • Kuize ZhangEmail author
  • Lijun Zhang
  • Lihua Xie
Chapter
Part of the Communications and Control Engineering book series (CCE)

Abstract

In Chap.  9, we studied the verification and complexity problem of the notions of strong detectability and weak detectability for finite-state automata. In this chapter, we characterize these notions for labeled Petri nets (see Sect.  2.4).

References

  1. Atig MF, Habermehl P (2009) On Yen’s path logic for Petri nets. In: Bournez O, Potapov I (eds) Reachability problems. Springer, Berlin, pp 51–63Google Scholar
  2. Cassandras CG, Lafortune S (2010) Introduction to discrete event systems, 2nd edn. Springer Publishing CompanyGoogle Scholar
  3. Dickson LE (1913) Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors. Am J Math 35(4):413–422MathSciNetCrossRefGoogle Scholar
  4. Hack M (1976) Petri net languages. Technical report Cambridge, MA, USAGoogle Scholar
  5. Li Z, Zhou M (2009) Deadlock resolution in automated manufacturing systems: a novel petri net approach, 1st edn. Springer Publishing CompanyGoogle Scholar
  6. Lipton RJ (1976) The reachability problem requires exponential space. Yale University. Department of computer science. Research report. Department of computer science, Yale UniversityGoogle Scholar
  7. Masopust T, Yin X (2019) Deciding detectability for labeled petri nets. Automatica 104:238–241MathSciNetCrossRefGoogle Scholar
  8. Mazaré L (2004) Using unification for opacity properties. Verimag Tech RepGoogle Scholar
  9. Rackoff C (1978) The covering and boundedness problems for vector addition systems. Theor Comput Sci 6(2):223–231MathSciNetCrossRefGoogle Scholar
  10. Reutenauer C (1990) The mathematics of petri nets. Upper Saddle River, Prentice-Hall Inc, NJ, USAzbMATHGoogle Scholar
  11. Saboori A, Hadjicostis CN (2013) Verification of initial-state opacity in security applications of discrete event systems. Inf Sci 246:115–132MathSciNetCrossRefGoogle Scholar
  12. Seatzu C, Silva M, van Schuppen JH (eds) (2013) Control of discrete-event systems: automata and petri-net perspectives. Lecture notes in control and information sciences, vol 433. Springer, London, p 478Google Scholar
  13. Tong Y et al (2017) Decidability of opacity verification problems in labeled Petri net systems. Automatica 80:48–53MathSciNetCrossRefGoogle Scholar
  14. Yen HC (1992) A unified approach for deciding the existence of certain petri net paths. Inf Comput 96(1):119–137MathSciNetCrossRefGoogle Scholar
  15. Zhang K, Giua A (2018) On detectability of labeled Petri nets and finite automata. https://arxiv.org/abs/1802.07551
  16. Zhang K, Giua A (2018) Weak (approximate) detectability of labeled petri net systems with inhibitor arcs. IFAC-PapersOnLine 51(7):167–171. 14th IFAC workshop on discrete event systems WODESCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of Electrical Engineering and Computer ScienceKTH Royal Institute of TechnologyStockholmSweden
  2. 2.School of Marine Science and TechnologyNorthwestern Polytechnical UniversityXi’anChina
  3. 3.School of Electrical and Electronic EngineeringNanyang Technological UniversitySingaporeSingapore

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