This Article 
 Bibliographic References 
 Add to: 
Timed Wp-Method: Testing Real-Time Systems
November 2002 (vol. 28 no. 11)
pp. 1023-1038

Abstract—Real-time systems interact with their environment using time constrained input/output signals. Examples of real-time systems include patient monitoring systems, air traffic control systems, and telecommunication systems. For such systems, a functional misbehavior or a deviation from the specified time constraints may have catastrophic consequences. Therefore, ensuring the correctness of real-time systems becomes necessary. Two different techniques are usually used to cope with the correctness of a software system prior to its deployment, namely, verification and testing. In this paper, we address the issue of testing real-time software systems specified as a Timed Input Output Automaton (TIOA). TIOA is a variant of timed automaton. We introduce the syntax and semantics of TIOA. We present the potential faults that can be encountered in a timed system implementation. We study these different faults based on TIOA model and look at their effects on the execution of the system using the region graph. We present a method for generating timed test cases. This method is based on a state characterization technique and consists of the following three steps: First, we sample the region graph using a suitable granularity, in order to construct a subautomaton easily testable, called Grid Automaton. Then, we transform the Grid Automaton into a Nondeterministic Timed Finite State Machine (NTFSM). Finally, we adapt the Generalized Wp-method to generate timed test cases from NTFSM. We assess the fault coverage of our test cases generation method and prove its ability to detect all the possible faults. Throughout the paper, we use examples to illustrate the various concepts and techniques used in our approach.

[1] R. Alur and D. Dill, "Automata for Modeling Real-Time Systems," Proc. 17th Int'l Colloq. Aut. Lang. Prog., 1990.
[2] R. Alur and D. Dill, “A Theory of Timed Automata,” Theoretical Computer Science, vol. 126, pp. 183-235, 1994.
[3] G.V. Bochmann, A. Das, R. Dssouli, M. Dubuc, A. Ghedamsi, and G. Luo, “Fault Model in Testing,” Proc. Fourth IFIP TC6 Int'l Workshop Protocol Test System, 1992.
[4] E. Brinksma, G. Scollo, and C. Steenbergen, “LOTOS Specification, Their Implementations and Their Tests,” Proc. Protocol Specification, Testing, and Verification, VI, B. Sarikaya and G. von Bochmann, eds., pp. 349–360, 1986.
[5] K. Cerans, “Decidability of Bisimulation Equivalences for Parallel Timer Processes,” Proc. Fourth Int'l Workshop Computer Aided Verification, G. von Bochmann and D.K. Probst, eds., pp. 302–315, 1992.
[6] O. Charles, “Application des Hypothésde Testáune Définition de la Couverture,” PhD thesis, UniversitéHenri Poincaré-Nancy 1, 1997.
[7] T.S. Chow, “Testing Software Design Modeled by Finite State Machine,” IEEE Trans. Software Eng., vol. 4, no. 3, pp. 178–187, 1978.
[8] D. Clarke and I. Lee, “Automatic Generation of Tests for Timing Constraints from Requirements,” Proc. Third Int'l Workshop Object-Oriented Real-Time Dependable Systems, Feb. 1997.
[9] R. Cardell-Oliver and T. Glover, “A Practical and Complete Algorithm for Testing Real-Time Systems,” Formal Techniques for Real-Time Fault Tolerant Systems, 1998.
[10] B. Dasarathy, “Timing Constraints of Real-Time Systems: Constructs for Expressing Them, Methods of Validating Them,” IEEE Trans. Software Eng., vol. 11, no. 1, pp. 80–86, Jan. 1985.
[11] R. De Nicola and M. Hennessy, “Testing Equivalences for Processes,” Theoretical Computer Science, vol. 34, pp. 83–133, 1984.
[12] C. Daws and S. Yovine, “Reducing the Number of Clock Variables of Timed Automata,” Proc. Real-Time Systems Symp., pp. 73-81, Dec. 1996.
[13] A. En-Nouaary, R. Dssouli, and A. Elqortobi, “Génération de Tests Temporisés,” Proc. Sixth Colloque Francophone de l'ingénierie des Protocoles, 1997.
[14] A. En-Nauaary, R. Dssaouli, F. Khendek, and A. Elqortobi, Timed Test Cases Generation Based on State Characterisation Technique Proc. IEEE Real-Time Systems Symp. (RTSS), pp. 220-229, Dec. 1998.
[15] A. En-Nouaary, F. Khendek, and R. Dssouli, “Fault Coverage in Testing Real-Time Systems,” Proc. Sixth Int'l Conf. Real-Time Systems Computing Systems and Applications (RTCSA '99), Dec. 1999.
[16] A. En-Nouaary, F. Khendek, and R. Dssouli, “Fault Coverage in Testing Real-Time Systems,” Technical Report TR-1162, Dept. IRO, Univ. de Montréal Sept. 1999.
[17] M.A. Fecko, P.D. Amer, M.U. Uyar, and A.Y. Duale, “Test Generation in the Presence of Conflicting Timers,” TESTCOM Aug./Sept. 2000.
[18] S. Fujiwara, V.G. Bochmann, F. Khendek, M. Amalou, and A. Ghedamsi, “Test Selection Based on Finite State Machine Model,” IEEE Trans. Software Eng., vol. 17, no. 6, pp. 591-603, June 1991.
[19] T. Higashino, A. Nakata, K. Taniguchi, and A. Cavalli, “Generating Test Cases for a Timed I/O Automaton Model,” Proc. Int'l Workshop Testing Communicating Systems (IWTCS '99), 1999.
[20] A. Khoumsi, M. Akalay, R. Dssouli, A. En-Nouaary, and L. Granger, “An Approach for Testing Real-Time Protocols,” TESTCOM, Aug./Sept. 2000.
[21] A. Khoumsi, A. En-Nouaary, R. Dssouli, and M. Akalay, “A New Method for Testing Real-Time Systems,” RTCSA, Dec. 2000.
[22] N.A. Lynch and H. Attiya, “Using Mappings to Prove Timing Properties,” Distributed Computing, vol. 6, no. 2, pp. 121–139, 1992.
[23] G. Luo, G.V. Bochman, and A. Petrenko, “Test Selection Based on Communicating Nodetermistic Finite State Machines Using a Generalized wp-Method,” IEEE Trans. Software Eng., vol. 20, no. 2, pp. 149-162, Feb. 1994.
[24] F. Liu, “Test Generation Based on an FSM Model with Timers and Counters,” master thesis, Dept. déInformatique et de Recherche Opérationnelle, Univ. de Montréal, 1993.
[25] K.G. Larsen and W. Yi, “Time Abstracted Bisimulation: Implicit Specification and Decidability,” Proc. Math. Foundations of Programming Semantics (MFPS 9), Apr. 1993.
[26] P. Merlin and D.J. Farber, Recoverability of Communication Protocols IEEE Trans. Comm., vol. 24, no. 9, Sept. 1976.
[27] D. Mandrioli, S. Morasca, and A. Morzenti, “Generating Test Cases for Real-Time Systems from Logic Specifications,” ACM Trans. Computer Systems, vol. 13, no. 4, pp. 365-398, Nov. 1995.
[28] B. Nielsen and A. Skou, “Automated Test Generation from Timed Automata,” Proc. Workshop Tools and Algorithms for the Construction and Analysis of Systems, Apr. 2001.
[29] X. Nicollin, J. Sifakis, and S. Yovine, “Compiling Real-Time Specifications into Extended Automata,” IEEE Trans. Software Eng., vol. 18, no. 9, pp. 794-804, Sept. 1992.
[30] K. Sabnani and A. Dahbura,“A protocol test generation procedure,”Comput. Networks and ISDN Syst.,vol. 15, pp. 285–297, 1988.
[31] J. Springintveld and F. Vaandrager, “Minimizable Timed Automata,” Proc. Fourth Int'l School and Symp. Formal Techniques in Real Time and Fault Tolerant Systems, B. Jonsson and J. Parrow, eds., 1996.
[32] J. Springintveld, F. Vaadranger, and P. Dargenio, “Testing Timed Automata,” Theoretical Computer Science, vol. 254, pp. 225–257, 2001.
[33] B. Taylor, “Introducing Real-Time Constraints into Requirements and High Level Design of Operating Systems,” Proc. Nat'l Telecomm. Conf., vol. 1, pp. 18.5.1–18.5.5, 1980.
[34] J. Tretmans, “A Formal Approach to Conformance Testing,” PhD Thesis, Univ. of Twente, Aug. 1992.
[35] J. Tretmans, “Testing Labelled Transition Systems with Inputs and Outputs,” Technical Report 95-26, University of Twente, Aug. 1995.
[36] S.T. Vuong and J. Curgus, “On Test Coverage Metrics for Communication Protocols,” Proc. Fourth Int'l Workshop Protocol Test System (IWPTS '91), Oct. 1991.
[37] S.T. Vuong, W.W.L. Chan, and M.R. Ito, “The UIOv Method for Protocol Test Sequence Generation,” Proc. Second Int'l Workshop Protocol Test System, 1989.
[38] S. Rapps and E.J. Weyuker, “Selecting Software Test Data Using Data Flow Information,” IEEE Trans. Software Eng., vol. 11, no. 4, pp. 367–375, Apr. 1985.
[39] M. Yao, “On the Development of Conformance Test Suites in View of Their Fault Coverage,” PhD thesis, Univ. de Montréal, Dept. IRO, 1995.

Index Terms:
Testing, specification, implementation, timed automaton, real-time systems, fault coverage.
Abdeslam En-Nouaary, Rachida Dssouli, Ferhat Khendek, "Timed Wp-Method: Testing Real-Time Systems," IEEE Transactions on Software Engineering, vol. 28, no. 11, pp. 1023-1038, Nov. 2002, doi:10.1109/TSE.2002.1049402
Usage of this product signifies your acceptance of the Terms of Use.