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Some concept of Computer Engineering are Binary Search, Byzantine Generals, Euclid Sequences, Houses and Utilities, Malfunction Diagnosis. Main points of this lecture are: Malfunction Diagnosis, Finding An Impostor, Medical Doctors, Opinions, Presented, Fake Coin Puzzle, Correct Judgment, Incorrect Judgment, Person Assessed, Impostors Around a Dinner Table

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2012/2013

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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
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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