Skip to main content
SpringerLink
Log in

Logical time control of concurrent DES

  • Published:
Discrete Event Dynamic Systems Aims and scope Submit manuscript

Abstract

The synthesis of controllers for reactive systems can be done by computing winning strategies in two-player games. Timed (game) Automata are an appropriate formalism to model real-time embedded systems but are not easy to use for controller synthesis for two reasons: i) timed models require the knowledge of the precise timings of the system; for example, if an action must occur in the future, the deadline of this occurrence must be known, ii) in practice, the dense state space makes the computation of the controller often impossible for complex systems. This paper introduces an extension of untimed game automata with logical time. The new semantics introduces two new types of uncontrollable actions: delayed actions which are possibly avoidable, and ineluctable actions which will eventually happen if nothing is done to abort it. The controller synthesis problem is adapted to this new semantics. This paper focuses specifically on the reachability and safety objectives and gives algorithms to generate a controller. The paper then extends these results to Game Petri Nets which can express concurrent timed behaviors and where an avoidable transition can lose its avoidability by the elapsing of time. The usefulness of this new model is illustrated by a real device driver synthesis example.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

Notes

  1. For this construction, ∀p ∈ P and ∀t ∈ T, Pre(p, t) = Post(p, t) = 0 except if it is explicitly set to 1.

  2. The model and the property to generate the strategy can be downloaded from https://github.com/jlbirccyn/JDEDS-Model

References

  • Altisen K, Tripakis S (2002) Tools for controller synthesis of timed systems. In: 2nd workshop on real-time tools (RT-TOOLS’2002)

  • Alur R, Dill DL (1994) A theory of timed automata. Theor Comput Sci 126(2):183–235

    Article  MathSciNet  Google Scholar 

  • Béchennec JL, Lime D, Roux OH (2019) Control of DES with urgency, avoidability and ineluctability. In: 19th international conference on application of concurrency to system design (ACSD’19)

  • Béchennec JL, Roux OH, Lime D (2019) Contrôle des SED avec urgence, évitabilité et inéluctabilité. In: Modélisation des Systèmes Réactifs (MSR’19), Modélisation des Systèmes Réactifs (MSR’19). Angers, France. https://hal.archives-ouvertes.fr/hal-02415319

  • Behrmann G, Cougnard A, David A, Fleury E, Larsen KG, Lime D (2007) Uppaal-tiga: Time for playing games!. In: Computer aided verification. Springer, pp 121–125

  • Bernet J, Janin D, Walukiewicz I (2002) Permissive strategies: from parity games to safety games. RAIRO - Theoretical Informatics and Applications (RAIRO:, ITA) 36:261–275

    Article  MathSciNet  Google Scholar 

  • Berthomieu B, Diaz M (1991) Modeling and verification of time dependent systems using time Petri nets. IEEE Trans Software Eng 17(3):259–273

    Article  MathSciNet  Google Scholar 

  • Berthomieu B, Vernadat F (2003) State class constructions for branching analysis of time petri nets. In: 9th international conference on tools and algorithms for the construction and analysis of systems (TACAS 2003), lecture notes in computer science, vol 2619. Springer, Warsaw, pp 442–457

  • Bornot S, Sifakis J (2000) An algebraic framework for urgency. Inf Comput 163(1):172–202

    Article  MathSciNet  Google Scholar 

  • Brandin BA, Wonham WM (1994) Supervisory control of timed discrete-event systems. IEEE Trans Autom Control 39(2):329–342

    Article  MathSciNet  Google Scholar 

  • Cassez F, David A, Fleury E, Larsen KG, Lime D (2005) Efficient on-the-fly algorithms for the analysis of timed games. In: CONCUR 2005–Concurrency theory. Springer, pp 66–80

  • Chatain Th, David A, Larsen KG (2009) Playing games with timed games. In: Giua A, Silva M, Zaytoon J (eds) Proceedings of the 3rd IFAC Conference on Analysis and Design of Hybrid Systems (ADHS’09). Zaragoza, Spain

  • Chatterjee K, de Alfaro L, Henzinger TA (2012) Strategy improvement for concurrent reachability and safety games coRR

  • De Alfaro L, Faella M, Henzinger TA, Majumdar R, Stoelinga M (2003) The element of surprise in timed games. In: CONCUR 2003-Concurrency theory. Springer, pp 144–158

  • De Alfaro L, Henzinger TA, Majumdar R (2001) Symbolic algorithms for infinite-state games. In: CONCUR 2001—Concurrency theory. Springer, pp 536–550

  • de Alfaro L, Henzinger TA, Kupferman O (2007) Concurrent reachability games. Theor Comput Sci 386(3):188–217

    Article  MathSciNet  Google Scholar 

  • Gardey G, Roux OF, Roux OH (2006) Safety control synthesis for time Petri nets. In: 8Th international workshop on discrete event systems (WODES’06). IEEE Computer Society Press, Ann Arbor, pp 222–228

  • Golaszewski C, Ramadge P (1987) Control of discrete event processes with forced events. In: Proceedings of the 26th conference on decision and control

  • Jard C, Lime D, Roux OH (2012) Clock transition systems. In: 21th international workshop on concurrency, specification and programming (CS&P 2012). Berlin, Germany

  • Lime D, Roux OH, Seidner C, Traonouez LM (2009) Romeo: A parametric model-checker for Petri nets with stopwatches. In: TACAS 2009, Lecture notes in computer science, vol 5505. Springer, York, pp 54–57

  • Maler O, Pnueli A, Sifakis J (1995) On the synthesis of discrete controllers for timed systems. In: STACS 95. Springer, pp 229–242

  • Microchip (2000) PIC18CXX8 Data Sheet (DS30475A). High-Performance Microcontrollers with CAN Module. http://ww1.microchip.com/downloads/en/DeviceDoc/30475a.pdf

  • Ramadge PJ, Wonham WM (1987) Supervisory control of a class of discrete event processes. SIAM J Control Optim 25(1):206–230

    Article  MathSciNet  Google Scholar 

  • Thomas W (1995) On the synthesis of strategies in infinite games. In: STACS 95. Springer, pp 1–13

  • Tripakis S, Altisen K (1999) On-the-fly controller synthesis for discrete and dense-time systems. In: FM’99, volume 1708 of LNCS. Springer Verlag, pp 233–252

  • Wonham WM, Ramadge PJ (1984) On the supremal controllable sublanguage of a given language. In: Decision and control, 1984. The 23rd IEEE conference on, vol 23, pp 1073–1080

Download references

Author information

Authors and Affiliations

  1. CNRS, LS2N, Nantes, France

    Jean-Luc Béchennec

  2. Ecole Centrale de Nantes, LS2N, Nantes, France

    Didier Lime & Olivier H. Roux

Authors
  1. Jean-Luc Béchennec
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Didier Lime
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Olivier H. Roux
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jean-Luc Béchennec.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article belongs to the Topical Collection: Topical Collection on Recent Trends in Reactive Systems

Guest Editor: Sebastian Lahaye

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Béchennec, JL., Lime, D. & Roux, O.H. Logical time control of concurrent DES. Discrete Event Dyn Syst 31, 185–217 (2021). https://doi.org/10.1007/s10626-020-00333-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10626-020-00333-x

Keywords

Search

Navigation