Publication 2003 Issue No. 7 - July Abstract - (t, k)-Diagnosable System: A Generalization of the PMC Models
(t, k)-Diagnosable System: A Generalization of the PMC Models
July 2003 (vol. 52 no. 7)
pp. 971-975
 ASCII Text x Toru Araki, Yukio Shibata, "(t, k)-Diagnosable System: A Generalization of the PMC Models," IEEE Transactions on Computers, vol. 52, no. 7, pp. 971-975, July, 2003.
 BibTex x @article{ 10.1109/TC.2003.1214345,author = {Toru Araki and Yukio Shibata},title = {(t, k)-Diagnosable System: A Generalization of the PMC Models},journal ={IEEE Transactions on Computers},volume = {52},number = {7},issn = {0018-9340},year = {2003},pages = {971-975},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2003.1214345},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - (t, k)-Diagnosable System: A Generalization of the PMC ModelsIS - 7SN - 0018-9340SP971EP975EPD - 971-975A1 - Toru Araki, A1 - Yukio Shibata, PY - 2003KW - Fault diagnosisKW - PMC modelKW - one-step t-diagnosisKW - sequential t-diagnosisKW - diagnosabilityKW - Cartesian product.VL - 52JA - IEEE Transactions on ComputersER -
Toru Araki, IEEE Computer Society

Abstract—In this paper, we introduce a new model for diagnosable systems called (t,k)-diagnosable system which guarantees that at least k faulty units (processors) in a system are detected provided that the number of faulty units does not exceed t. This system includes classical one-step diagnosable systems and sequentially diagnosable systems. We prove a necessary and sufficient condition for (t,k)-diagnosable system, and discuss a lower bound for diagnosability. Finally, we deal with a relation between (t,k)-diagnosability and diagnosability of classical basic models.

[1] F.P. Preparata, G. Metze, and R.T. Chien, On the Connection Assignment Problem of Diagnosable Systems IEEE Trans. Electronic Computers, vol. 16, no. 6, pp. 848-854, Dec. 1967.
[2] T. Araki and Y. Shibata, Diagnosability of Networks Represented by the Cartesian Product IEICE Trans. Fundamentals, vol. E83-A, no. 3, pp. 465-470, Mar. 2000.
[3] J.R. Armstrong and F.G. Gray, Fault Diagnosis in a Boolean$n$Cube Array of Microprocessors IEEE Trans. Computers, vol. 30, no. 8, pp. 587-596, Aug. 1981.
[4] M.A. Barborak, M. Malek, and A.T. Dahbura, "The Consensus Problem in Fault-Tolerant Computing," ACM Computer Surveys, vol. 25, pp. 171-220, June 1993.
[5] K.-Y. Chwa and L. Hakimi, On Fault Identification in Diagnosable Systems IEEE Trans. Computers, vol. 30, no. 6, pp. 414-422, June 1981.
[6] A. Das, K. Thulasiraman, and V.K. Agarwal, Diagnosis of$t/(t+1){\hbox{-}}{\rm Diagnosable}$Systems SIAM J. Computing, vol. 23, no. 5, pp. 895-905, May 1994.
[7] A.D. Friedman, A New Measure of Digital System Diagnosis Proc. 1975 Int'l Symp. Fault-Tolerant Computing, pp. 167-170, June 1975.
[8] S.L. Hakimi and A.T. Amin, Characterization of Connection Assignment of Diagnosable Aystems IEEE Trans. Computers, vol. 23, no. 1, pp. 86-88, Jan. 1974.
[9] H. Fujiwara and K. Kinoshita, On the Computational Complexity of System Diagnosis IEEE Trans. Computers, vol. 27, no. 10, pp. 881-885, Oct. 1978.
[10] S. Khanna and W.K. Fuchs, A Linear Time Algorithm for Sequential Diagnosis in Hypercubes J. Parallel and Distributed Computing, vol. 26, pp. 48-53, 1995.
[11] S. Khanna and W.K. Fuchs, A Graph Partitioning Approach to Sequential Diagnosis IEEE Trans. Computers, vol. 46, no. 1, pp. 39-47, Jan. 1997.
[12] T. Kohda, A Simple Discriminator for Identifying Faults in Highly Structured Diagnosable Systems J. Circuits, Systems, and Computers. vol. 4, no. 3, pp. 255-277, Sept. 1994.
[13] J.-K. Lee and J.T. Butler, A Characterization of$t/s{\hbox{-}}{\rm Diagnosability}$and Sequential$t{\hbox{-}}{\rm Diagnosability}$in Designs IEEE Trans. Computers, vol. 39, no. 10, pp. 1298-1304, Oct. 1990.
[14] S. Mallela and G.M. Masson, Diagnosable Systems for Intermittent Faults IEEE Trans. Computers, vol. 27, no. 6, pp. 560-566, June 1978.
[15] U. Manber, System Diagnosis with Repair IEEE Trans. Computers, vol. 29, no. 10, pp. 934-937, Oct. 1980.
[16] V. Raghavan and A.R. Tripathi, Sequential Diagnosability is Co-NP Complete IEEE Trans. Computers, vol. 40, no. 2, pp. 584-595, Feb. 1991.
[17] Y. Shibata and S. Iijima, Synthesis and Diagnosis Algorithms of Diagnosable Systems on de Bruijn Networks and Kautz Networks Denshi Joho Tsushin Gakkai Ronbunshi, vol. J75-D-I, no. 12, pp. 1144-1153, Dec. 1992.
[18] A.K. Somani, “Sequential Fault Occurence and Reconfiguration in System Level Diagnosis,” IEEE Trans. Computers, vol. 39, no. 12, pp. 1,472-1,475, Dec. 1990.
[19] A.K. Somani, V.K. Agarwal, and D. Avis, "A Generalized Theory for System Level Diagnosis," IEEE Trans. Computers, vol. 36, no. 5, pp. 538-546, May 1987.
[20] A.K. Somani and O. Peleg, On Diagnosability of Large Fault Sets in Regular Topology-Based Computer Systems IEEE Trans. Computers, vol. 45, no. 8, pp. 892-903, Aug. 1996.
[21] J. Xu and S. ze Huang, Sequentially$t{\hbox{-}}{\rm Diagnosable}$Systems: A Characterization and Its Applications IEEE Trans. Computers, vol. 44, no. 2, pp. 340-345, Feb. 1995.
[22] C.L. Yang, G.M. Masson, and R.A. Leoneti, "On Fault Isolation and Identification in t1/t1-Diagnosable Systems," IEEE Trans. Computers, vol. 35, no. 7, pp. 639-643, July 1986.

Index Terms:
Fault diagnosis, PMC model, one-step t-diagnosis, sequential t-diagnosis, diagnosability, Cartesian product.
Citation:
Toru Araki, Yukio Shibata, "(t, k)-Diagnosable System: A Generalization of the PMC Models," IEEE Transactions on Computers, vol. 52, no. 7, pp. 971-975, July 2003, doi:10.1109/TC.2003.1214345