Abstract
Real-time discrete event systems are discrete event systems with timing constraints, and can be modeled by timed automata. The latter are convenient for modeling real-time discrete event systems. However, due to their infinite state space, timed automata are not suitable for studying real-time discrete event systems. On the other hand, finite state automata, as the name suggests, are convenient for modeling and studying non-real time discrete event systems. To take into account the advantages of finite state automata, an approach for studying real-time discrete event systems is to transform, by abstraction, the timed automata modeling them into finite state automata which describe the same behaviors. Then, studies are performed on the finite state automata model by adapting methods designed for non real-time discrete event systems. In this paper, we present a method for transforming timed automata into special finite state automata called Set-Exp automata. The method, called SetExp, models the passing of time as real events in two types: Set events which correspond to resets with programming of clocks, and Exp events which correspond to the expiration of clocks. These events allow to express the timing constraints as events order constraints. SetExp limits the state space explosion problem in comparison to other transformation methods of timed automata, notably when the magnitude of the constants used to express the timing constraints are high. Moreover, SetExp is suitable, for example, in supervisory control and conformance testing of real-time discrete event systems.
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References
Alur R (1999) Timed automata. In: 11th international conference on computer aided verification. Lecture notes in computer science, vol 1633. Springer, Berlin, pp 8–22
Alur R, Dill D (1994) A theory of timed automata. Theor Comput Sci 126, 183–235
Alur R, Henzinger TA (1991) Logic and models of real time: a survey. In: de Bakker JW, Huizing C, de Rover W-P, Rozenberg G (eds) Real-time: theory in practice REX workshop proceedings. LNCS, vol 600. Springer, Berlin, pp 74–106
Alur R, Courcoubetis C, Halbwachs N, Dill D, Wong-Toi H (1992) Minimization of timed transitions systems. In: CONCUR, pp 340–354
Asarin E, Maler O, Pnueli A, Sifakis J (1998) Controller synthesis for timed automata. In: IFAC symposium on system structure and control, pp 469–474
Behrmann G, Bouyer P, Larsen KG, Pelánek R (2004a) Lower and upper bounds in zone based abstractions of timed automata. In: TACAS, pp 312–326
Behrmann G, David R, Larsen KG (2004b) A tutorial on uppaal. In: Proc formal methods for the design of real-time systems (SFM-RT 2004). Lecture notes in computer science, vol 3185. Springer, Berlin, pp 200–236
Bengtsson J, Yi W (2004) Timed automata: semantics, algorithms and tools. In: Reisig W, Rozenberg G (eds) Lectures notes on concurrency and Petri nets. LNCS, vol 3098. Springer, Berlin, pp 87–124
Bérard B, Diekert V, Gastin P, Petit A (1998) Characterization of the expressive power of silent transitions in timed automata. Fundam Inform 36(2), 145–182
Brandin BA, Wonham WM (1994) Supervisory control of timed discrete-event systems. IEEE Trans Autom Control 39(2), 329–342
Carroll J, Long JD (1989) Theory of finite automata. Prentice-Hall, New York
Daws C, Yovine S (1996) Reducing the number of clock variables of timed automata. In: Proceedings, 17th IEEE real-time systems symposium. IEEE Computer Society Press, Los Alamitos, pp 73–81
Dill D (1990) Timing assumptions and verification of finite-state concurrent systems. In: Sifakis J (ed) Proc automatic verification methods for finite state systems. LNCS, vol 407. Springer, Berlin, pp 197–212
El Ghazouani K, Nourelfath M, En-Nouaary A, Dssouli R (2002) Diagnostic de fautes de transfert simples dans les systèmes temps réel modélisés par des automates entríe-sortie temporisés. In: Colloque Francophone sur l’ingínierie des protocoles (CFIP’02), Hermes-Lavoisier, May 2002, pp 195–208
En-Nouaary A (2007) A scalable method for testing real-time systems. Int J Softw Qual 16, 3–22
En-Nouaary A, Dssouli R, Khendek F, Elqortobi A (1998) Timed test cases generation based on state characterization technique. In: IEEE real-time systems symposium, December 1998, p 220
En-Nouaary A, Dssouli R, Khendek F (2002) Timed wp-method: Testing real-time systems. IEEE Trans Softw Eng 28(11), 1023–1038
Henzinger TA, Nicollin X, Sifakis J, Yovine S (1994) Symbolic model checking for real-time systems. J Inf Comput 111(2), 193–244
Ho T-J (2003) A method for the modular synthesis of controllers for timed discrete-event systems. Int J Control 76(5), 520–535
Hopcroft JE, Ullman JD (1979) Introduction to automata theory, language and computation. Addison-Wesley, Reading
Kang I, Lee I (1994) State minimization for concurrent system analysis based on state space exploration. In: Proceedings of conference on computer assurance, pp 123–134
Kang I, Lee I (1996) An efficient state space generation for analysis of real-time systems. In: Proceedings of international symposium on software testing and analysis (ISSTA’96), pp 4–13
Khoumsi A (2002) A method for testing the conformance of real-time systems. In: IEEE international symposium on formal techniques in real-time and fault-tolerent systems (FTRTFT), Oldenburg, Germany, September 2002. Springer, Berlin, pp 331–354
Khoumsi A (2004) Complete test graph generation for symbolic real-time systems. In: Proc Brazilian symposium on formal methods (SBMF 2004). Electronic notes in theoretical computer science, vol 130, Recife, Brazil, November 2004, pp 79–100. http://www.gel.usherbrooke.ca/khoumsi/Research/Public/SBMF04-Test.pdf
Khoumsi A (2005) A supervisory control method for ensuring the conformance of real-time discrete event systems. J Discrete Event Dyn Syst 15(4), 397–431
Khoumsi A, Ouedraogo L (2004) A new method for transforming timed automata. In: Proc Brazilian symposium on formal methods (SBMF 04). Electronic notes in theoretical computer science, vol 130. Recife, Brazil, November 2004, pp 101–128
Khoumsi A, Ouedraogo L (2009) Diagnosis of faults in real-time discrete event systems. In: IFAC symposium on fault detection, supervision and safety of technical processes (SafeProcess), July 2009
Khoumsi A, Ouedraogo L, Nourelfath M (2005) Supervisory control of real-time discrete event systems modeled by timed automata with invariants. In: IASTED international conference on intelligent systems and control (ISC), Cambridge, MA, USA, October 2005
Larsen KG, Pettersson P, Yi Y (1997) Uppaal: status & developments. In: Proceedings of the 9th international conference on computer aided-verification, Haifa, Israel, June 1997, pp 456–459
Larsen KG, Yi W (1997) Time abstracted bisimulation: implicit specifications and decidability. Inf Comput 134(2), 75–101
Nourelfath M, Khoumsi A (2006) Grid automata and supervisory control of dense real-time discrete event systems. Math Comput Simul 70(5), 408–418
Ostroff JS (1990) Deciding properties of timed transition models. IEEE Trans Parallel Distrib Syst 1(2), 170–183
Ostroff JS, Wonham WM (1990) A framework for real-time discrete event control. IEEE Trans Autom Control 35(4), 386–397
Ouedraogo L, Khoumsi A, Nourelfath M (2006a) Méthode de transformation d’automates temporisés avec invariants de localités. In: Conférence francophone de modélisation et simulation (MOSIM), Rabat, Morroco, April 2006
Ouedraogo L, Nourelfath M, Khoumsi A (2006b) A new method for centralized and modular supervisory control of real-time discrete event systems. In: IEEE international workshop on discrete event systems (WODES), Ann Arbor, MI, USA, July 2006, pp 168–175
Ouedraogo L, Khoumsi A, Nourelfath M (2010) A new method for centralized and modular supervisory control of real-time discrete event systems. Int J Control 83(1), 1–39
Pappas GJ (2003) Bisimilar linear systems. Automatica 39(12), 2035–2047
Ramadge PJ, Wonham WM (1987) Supervisory control of a class of discrete event processes. SIAM J Control Optim 25(1), 206–230
Ramadge PJ, Wonham WM (1989) The control of discrete event systems. Proc IEEE 77, 81–98
Sampath M, Sengupta R, Lafortune S, Sinnamohideen K, Teneketzis D (1995) Diagnosability of discrete-event systems. IEEE Trans Autom Control 40(9), 1555–1575
Sampath M, Sengupta R, Lafortune S, Sinnamohideen K, Teneketzis D (1996) Failure diagnosis using discrete-event model. IEEE Trans Control Syst Technol 4(2), 105–124
Springintveld J, Vaadranger F, Dargenio P (2001) Testing timed automata. Theor Comput Sci 254, 225–257
Tretmans J (1996) Test generation with inputs, outputs and repetitive quiescence. Softw Concepts Tools 17(3):103–120
Tripakis S, Yovine S (2001) Analysis of timed systems using time-abstraction bisimulations. Form Methods Syst Des 18(1), 25–68
Wong-Toi H, Hoffmann G (1991) The control of dense real-time discrete event systems. In: Proc of 30th IEEE conference on decision and control. Brighton, England, pp 1527–1528
Yamalidou EC, Patsidou EP, Kantor JC (1990) Modelling discrete-event dynamical systems for chemical process control—a survey of several new techniques. Comput Chem Eng 14(3), 281–299
Yannakakis M, Lee D (1993) An efficient algorithm for minimizing real-time transition systems. In: Proceedings, fifth international conference on computer aided verification. LNCS, vol 697. Springer, Berlin, pp 210–224
Yovine S (1997) Kronos: a verification tool for real-time systems. Int J Softw Tools Technol Transf 1(1–2), 123–133
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Ouedraogo, L., Khoumsi, A. & Nourelfath, M. SetExp: a method of transformation of timed automata into finite state automata. Real-Time Syst 46, 189–250 (2010). https://doi.org/10.1007/s11241-010-9103-8
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DOI: https://doi.org/10.1007/s11241-010-9103-8