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Fast diagnosis of multiprocessor systems with random faults. (English) Zbl 0803.68004
Summary: Processors in a multiprocessor system fail independently with constant probability \(0< p< 1/2\). They can test one another and faulty processors have to be identified on the basis of test results. Fault-free processors diagnose other fault-free processors correctly and find faults in faulty ones with probability \(q\leq 1\) in each test. Faulty testers are unreliable: they may even behave maliciously. Tests are independent and in every time unit a processor can be involved in at most one test. We propose testing schemes which are fast, use few tests and are correct with probability converging to 1 as the size of the system grows.

68M15 Reliability, testing and fault tolerance of networks and computer systems
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[1] 1. D. ANGLUIN and L. G. VALIANT, Fast Probabilistic Algorithms for Hamiltonian Circuits and Matchings, J. Comput. System Sci., 1979, 18, pp. 155-193. Zbl0437.05040 MR532174 · Zbl 0437.05040 · doi:10.1016/0022-0000(79)90045-X
[2] 2. R. BEIGEL, S. R. KOSARAJU and G. F. SULLIVAN, Locating Faults in a Constant Number of Parallel testing Rounds, in Proceedings of the 1989 ACM Symposium on Parallel Algorithms and Architectures, pp. 189-198.
[3] 3. P. BERMAN and A. PELC, Distributed Probabilistic Fault Diagnosis for Multiprocessor Systems, Digest of Papers, FTCS-20, 1990, pp. 340-346.
[4] 4. D. M. BLOUGH, Fault Detection and Diagnosis in Multiprocessor Systems, Ph. D. Thesis, The John Hopkins University, 1988.
[5] 5. D. M. BLOUGH, G. F. SULLIVAN and G. M. MASSON, Almost Certain Diagnosis for Intermittenly Faulty Systems, Digest of Papers, FTCS-18, 1988, pp. 260-271.
[6] 6. D. M. BLOUGH, G. F. SULLIVAN and G. M. MASSON, Fault Diagnosis for Sparsely Interconnected Multiprocessor Systems, Digest of Papers, FTCS-19, 1989, pp. 62-69.
[7] 7. M. L. BLOUNT, Probabilistic Treatment of Diagnosis in Digital Systems, Digest of Papers, FTCS-7, 1077, pp. 72-77.
[8] 8. A. T. DAHBURA, System-Level Diagnosis: a Perspective for the Third Decade, in Concurrent Computation: Algorithms, Architectures, Technologies, Plenum Publ. Corp., 1988.
[9] 9. A. T. DAHBURA, K. K. SABNANI and L. L. KING, The Comparison Approach to Multiprocessor Fault Diagnosis, IEEE Trans. Comput., March 1987, 36, pp. 373-378.
[10] 10. D. FUSSELL and S. RANGARAJAN, Probabilistic Diagnosis of Multiprocessor Systems with Arbitrary Connectivity, Digest of Papers, FTCS-19, 1989, pp. 560-565.
[11] 11. T. HAGERUP and Ch. RÜB, A Guided Tour of Chernoff Bounds, Inf. Proc. Lett., 1989/1990, 33, pp. 305-308. Zbl0702.60021 MR1045520 · Zbl 0702.60021 · doi:10.1016/0020-0190(90)90214-I
[12] 12. S. N. MAHESHWARI and S. L. HAKIMI, On Models for Diagnosable Systems and Probabilistic Fault Diagnosis, IEEE Trans. Comput., March 1976, 25, pp. 228-236. Zbl0339.68047 MR530234 · Zbl 0339.68047 · doi:10.1109/TC.1976.5009249
[13] 13. F. P. PREPARATA, R. T. CHIEN, On the Connection Assignment Problem of Diagnosable Systems, IEEE Trans. Electr. Comput., December 1967, 16, pp. 848-854. Zbl0189.16904 · Zbl 0189.16904 · doi:10.1109/PGEC.1967.264747
[14] 14. S. RANGARAJAN and D. FUSSEL, A Probabilistic Method for Fault Diagnosis of Multiprocessor Systems, Digest of Papers, FTCS-18, 1988, pp. 278-283.
[15] 15. E. R. SCHEINERMAN, Almost Sure Fault Tolerance in Random Graphs, SIAM J. Comput., 1987, 16, pp. 1124-1134. Zbl0654.68015 MR917044 · Zbl 0654.68015 · doi:10.1137/0216071
[16] 16. E. SCHMEICHEL, S. L. HAKIMI, M. OTSUKA and G. SULLIVAN, On Minimizing Testing Rounds for Fault Identification, Digest of Papers, FTCS-18, 1988, pp. 266-271.
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