Malfunction Diagnosis - Computer Engineering - Lecture Slides, Slides of Computer Science

Download Malfunction Diagnosis - Computer Engineering - Lecture Slides and more Slides Computer Science in PDF only on Docsity! Malfunction Diagnosis Ten Puzzling Problems in Computer Engineering Docsity.com PORT TECH SUP SB URNS "Sizzling...smoking...flames shooting from the hard drive. OK...that IS a malfunction and you'd best unplug it." "Tn afraid your problem is a serious nisprin{ in TO HAVE $800 SPENT ON iT.” your dome-medical guide." (® Docsity.com “ ACCORDING To OUR. DIAGNOSTIC COMPUTER, YOUR CAR WANTS Analysis for a Given Set of Outcomes In each of the cases shown below, determine the smallest possible number of impostors that would be consistent with the shown outcome Y Y Y Y Y Y Y Y N N N N N N N N Y Y Y Y N N N N N N Y Y N Y Y N 0 What is the largest possible number of non-impostors? B G B G G B B G Generalize to ring of arbitrary size, even or odd All Ns good All Ys bad: Is 4 smallest possible? ??? Generalize to ring of arbitrary even size Docsity.com Finding Impostors with Limited Questioning At a party, 10 people of a certain group (say, science-fiction writers) try to determine if there are impostors among them. Each person is asked a question by 2 different people and there are at most 3 impostors. Can the impostors be always correctly identified from the outcomes of the 20 questions? Solve the puzzle in the following two cases: Case 1: It is possible for persons A and B to ask each other questions Case 2: If A asks B a question, then B will not ask A a question Can’t be done. Ten people around a dinner table is a special case of this, because each person is questioned by his/her two neighbors. In that case, we determined that no more than 2 impostors can be identified Can’t be done. If you switch the reals and impostors in the 6-person cluster, exactly the same syndrome may be observed Another reason Docsity.com Malfunction Diagnosis Model Layered approach to self-diagnosis A small core part of a unit is tested Trusted core tests the next layer of subsystems Sphere of trust is gradually extended Diagnosis of one unit by another The tester sends a self-diagnosis request, expecting a response The unit under test eventually sends some results to the tester The tester interprets the results received and issues a verdict Testing capabilities among units is represented by a directed graph i Tester j Testee Test capability I think j is good (passed test) 0 i Tester j Testee Test capability I think j is bad (failed test} 1 The verdict of unit i about unit j is denoted by Dij ∈ {0, 1} All the diagnosis verdicts constitute the n × n diagnosis matrix D Core Docsity.com Sequential t-Diagnosability An n-unit system is sequentially t-diagnosable if the diagnosis syndromes when there are t or fewer malfunctions are such that they always identify, unambiguously, at least one malfunctioning unit Necessary condition: n ≥ 2t + 1; i.e., a majority of units must be good This is useful because some systems that are not 1-step t-diagnosable are sequentially t-diagnosable, and they can be restored by removing the identified malfunctioning unit(s) and repeating the process This system is sequentially 2-diagnosable In one step, it is only 1-diagnosable Sequential diagnosability of directed rings: An n-node directed ring is sequentially t-diagnosable for any t that satisfies (t2 – 1)/4 + t + 2 ≤ n M0 M1 M4 M2 M3 D01 D12 D34 D23 D40 Docsity.com Syndromes for M0 bad: 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 Sequential 2-Diagnosability Example Consider this system, with the test outcomes shown The system above is sequentially 2-diagnosable (we can correctly diagnose up to two malfunctioning units, but only one at a time) Malfunction syndromes (x means 0 or 1) Malfn D01 D12 D23 D34 D40 M0 x 0 0 0 1 M1 1 x 0 0 0 M2 0 1 x 0 0 M3 0 0 1 x 0 M4 0 0 0 1 x M0,M1 x x 0 0 1 M0,M2 x 1 x 0 1 M0,M3 x 0 1 x 1 M0,M4 x 0 0 1 x M0 M1 M4 M2 M3 D01 D12 D34 D23 D40 Docsity.com A Related Puzzle: Blue-Eyed Islanders Inhabitants of an island are blue-eyed or brown-eyed, but none of them knows the color of his/her own eyes, and must commit ritual suicide the next day at noon if s/he ever finds out. [Okay, this is silly, but don’t argue with the premises, such as there not being any mirrors, etc.; just view it as an exercise in logical reasoning.] The islanders are quite proficient in logical reasoning and won’t miss a chance to deduce their eye color, should there be enough info to do so. Unaware of the islanders’ traditions, which make discussing eye colors a taboo, a visitor giving a speech on the island begins his speech thus: “It’s so good to see someone else with blue eyes on this island.” What are the consequences of this faux-pas? Hint: Begin by thinking about what would happen if there were just one blue-eyed islander and build up to larger numbers of blue-eyed people. Docsity.com