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Detectability of Finite-State Automata

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

Abstract

A finite-state automaton (FSA) (see Sect. 2.3) is obtained from a standard nondeterministic finite automaton (NFA, see Sect. 1.3) by removing all accepting states and also replacing the unique initial state by a set of initial states. Such a modification can be used to better describe discrete-event systems (DESs) (Wonham and Cai 2019; Cassandras and Lafortune 2010). DESs usually refer to as event-driven processes that cannot be described by differential equations, where the latter usually represent time-driven processes. The FSA-based DESs are usually simple and many properties of FSAs are decidable, so FSAs are rather welcome in engineering-oriented studies. However, despite being simple, FSAs can also perform many good properties that are of both theoretical and practical importance. During the past three decades, plenty of properties and their verification or synthesis techniques on DESs in the framework of FSAs have been proposed and developed, e.g., controllability and observability (The notion of observability in the supervisory control framework is totally different from that studied in this book (see Chaps.  4,  5,  7).) (Ramadge and Wonham 1987; Ramadge 1986; Lin and Wonham 1988), diagnosability (Lin 1994; Sampath 1995), detectability (Shu et al. 2007; Shu and Lin 2011; Zhang 2017), opacity (Saboori and Hadjicostis 2014, 2012, 2011, 2013; Lin 2011), etc., where controllability and observability are defined on formal languages, diagnosability is defined on events, but the others are defined on states (except for that the result of Lin (2011) is defined on formal languages).

References

  1. Cassandras CG, Lafortune S (2010) Introduction to discrete event systems, 2nd edn. Springer Publishing CompanyGoogle Scholar
  2. Lafortune S, Lin F (2017) From diagnosability to opacity: a brief history of diagnosability or lack thereof. IFAC-PapersOnLine 50(1):3022–3027CrossRefGoogle Scholar
  3. Lin F (1994) Diagnosability of discrete event systems and its applications. Discret Event Dyn Syst 4(2):197–212CrossRefGoogle Scholar
  4. Lin F (2011) Opacity of discrete event systems and its applications. Automatica 47(3):496–503MathSciNetCrossRefGoogle Scholar
  5. Lin F, Wonham WM (1988) On observability of discrete-event systems. Inf Sci 44(3):173–198MathSciNetCrossRefGoogle Scholar
  6. Masopust T (2018) Complexity of deciding detectability in discrete event systems. Automatica 93:257–261MathSciNetCrossRefGoogle Scholar
  7. Mazaré L (2004) Using unification for opacity properties. Verimag Tech RepGoogle Scholar
  8. Ramadge PJ (1986) Observability of discrete event systems. In: 1986 25th IEEE conference on decision and control, pp 1108–1112Google Scholar
  9. Ramadge PJ, Wonham WM (1987) Supervisory control of a class of discrete event processes. SIAM J Control Optim 25(1):206–230MathSciNetCrossRefGoogle Scholar
  10. Saboori A, Hadjicostis CN (2014) Current-state opacity formulations in probabilistic finite automata. IEEE Trans Autom Control 59(1):120–133MathSciNetCrossRefGoogle Scholar
  11. Saboori A, Hadjicostis CN (2012) Verification of infinite-step opacity and complexity considerations. IEEE Trans Autom Control 57(5):1265–1269MathSciNetCrossRefGoogle Scholar
  12. Saboori A, Hadjicostis CN (2013) Verification of initial-state opacity in security applications of discrete event systems. Inf Sci 246:115–132MathSciNetCrossRefGoogle Scholar
  13. Saboori A, Hadjicostis CN (2011) Verification of K-step opacity and analysis of its complexity. IEEE Trans Autom Sci Eng 8(3):549–559CrossRefGoogle Scholar
  14. Sampath M et al (1995) Diagnosability of discrete-event systems. IEEE Trans Autom Control 40(9):1555–1575MathSciNetCrossRefGoogle Scholar
  15. Seatzu C, Silva M, van Schuppen JH (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
  16. Shu S, Lin F (2011) Generalized detectability for discrete event systems. Syst Control Lett 60(5):310–317MathSciNetCrossRefGoogle Scholar
  17. Shu S, Lin F, Ying H (2007) Detectability of discrete event systems. IEEE Trans Autom Control 52(12):2356–2359MathSciNetCrossRefGoogle Scholar
  18. Wonham WM, Cai K (2019) Supervisory control of discrete-event systems. Springer International PublishingGoogle Scholar
  19. Zhang K (2017) The problem of determining the weak (periodic) detectability of discrete event systems is PSPACE-complete. Automatica 81:217–220MathSciNetCrossRefGoogle Scholar
  20. Zhang K, Giua A (2018) On detectability of labeled Petri nets and finite automata. https://arXiv.org/abs/1802.07551

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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