臺灣博碩士論文加值系統

系統偵錯(system-level diagnosis)是根據系統中各個處理器相互測試的結果，
推導出系統中錯誤處理器的程序。(t, k)偵錯是循序偵錯的概念化，當系統最多存
在t 個錯誤處理器時，在每一次進行偵錯時，至少須辨識出k 個錯誤處理器並且
以正常的處理器更換之。本篇論文假設每個處理器至少與一個正常處理器相鄰，
證明圖形在MM*模式下的(t, k)-條件式偵錯能力。

System-level diagnosis is used to identify faulty processors. Each processor in the
system can test its neighboring processors and declare them fault-free or faulty. And
(t, k)-diagnosis is an conceptualization of sequential diagnosis. In (t, k)-diagnosis, at
least k faulty processors (or all faulty processors if fewer than k faulty processors
remain) are identified and repaired in each iteration provided there are at most t faulty
processors. In this paper, it assumes that each processor neighbor to at least one
fault-free processor. We prove the conditional (t, k)-diagnosability of the r-regular
graph under the MM* model.

Contents iv
List of Figures v
List of Tables vi
1 Introduction 1
2 Preliminaries 4
3 Conditional (t, k)-diagnosis with fathomed component 9
4 Conditional (t, k)-diagnosis without fathomed component 12
5 Main result and applications 23
6 Discussion and conclusion 25

[1] T. Araki and Y. Shibata, "(t, k)-diagnosable system: a generalization of the PMC models," IEEE Transactions on Computers, vol. 52, no. 7, pp. 971-975, 2003.
[2] G. Y. Chang, G. H. Chen, and G. J. Chang, "(t, k)-diagnosis for matching composition
networks," IEEE Transactions on Computers, vol. 55, no. 1, pp. 88-92, 2006.
[3] G. Y. Chang, G. H. Chen, and G. J. Chang, "(t, k)-diagnosis for matching composition networks under the MM* model," IEEE Transactions on Computers, vol. 56,no. 1, pp. 73-79, 2007.
[4] G. Y. Chang and G. H. Chen, "(t, k)-diagnosability of multiprocessor systems with applications to grids and tori," SIAM Journal on Computing, vol. 37, no. 4, pp. 1280-1298, 2007.
[5] G. Y. Chang "Conditional (t, k)-Diagnosis under the PMC Model" IEEE Transactions on parallel and distributed systems, vol. 22, no. 11, 2011.
[6] K. Day, "The conditional node connectivity of the k-ary n-cube," Journal of Interconnection Networks, vol. 5, no.1, pp. 13-26, 2004.
[7] A. H. Esfahanian, "Generalized measures of fault tolerance with application to N-cube networks," IEEE Transactions on Computers, vol. 38, no. 11, pp. 1586-1591,
1989.
[8] J. Fan, "Diagnosability of the Möbius cubes," IEEE Transactions on Parallel and
Distributed Systems, vol. 9, no. 9, pp. 923-927, 1998.
[9] S. Khanna and W. K. Fuchs, "A graph partitioning approach to sequential diagnosis,"IEEE Transactions on Computers, vol. 46, no. 1, pp. 39-47, 1997.
[10] S. P. Kuo, H. J. Kuo, and Y. C. Tseng, "The beacon movement detection problem in wireless sensor networks for localization applications," IEEE Trans. on Mobile Computing, vol. 8 no.10, pp. 1326-1338, 2009.
[11] P. L. Lai, J. M. Tan, C. P. Chang, and L. H. Hsu, "Conditional diagnosability measures for large multiprocessor systems," IEEE Transactions on Computers, vol. 54, no. 2,pp. 165-175, 2005.
[12] Q. Li and Y. Zhang, "Restricted connectivity and restricted fault diameter of some interconnection networks," DIMACS Series in Discrete Mathematics and Theoretical
Computer Science, vol. 21, pp. 267-273, 1995.
[13] F. P. Preparata, G. Metze, and R. T. Chien, "On the connection assignment problem
of diagnosable systems," IEEE Transactions on Electronic Computers, vol. EC-16,pp. 848-854, 1967.
[14] S. Y. Hsieh and Y. S. Chen, ``Strongly diagnosable systems under the comparison diagnosis model,'' IEEE Transactions on Computers, vol. 57, no. 12, pp. 1720-1725,
2008.
[15] D. Wang, "Diagnosability of enhanced hypercubes," IEEE Transactions on Computers,vol. 43, no. 9, pp. 1054-1061, 1994.
[16] Q. Zhu, S. Y. Liu, and M. Xu, "On conditional diagnosability of the folded hypercubes,"Information Sciences, vol. 45, pp.174-184, 2008.