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The Byzantine Generals Problem Leslie Lamport, Robert Shostak and Marshall Pease Presenter: Phyo Thiha Date: 4/1/2008.

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Presentation on theme: "The Byzantine Generals Problem Leslie Lamport, Robert Shostak and Marshall Pease Presenter: Phyo Thiha Date: 4/1/2008."— Presentation transcript:

1 The Byzantine Generals Problem Leslie Lamport, Robert Shostak and Marshall Pease Presenter: Phyo Thiha Date: 4/1/2008

2 Introduction Why this problem?  Computer Systems Reliability Security

3 Initial Conditions 1.ALL loyal lieutenants obey the same order. 2.IF commanding general is loyal  EVERY loyal lieutenant obeys the order he sends.

4 Impossibility Results Valid for oral messages NO solution for generals < 3m+1 Commander Lieutenant 1 Lieutenant 2 attack C  L2: retreat attack Fig. 1. Lieutenant as traitor

5 Commander Lieutenant 1 Lieutenant 2 attack C  L2: retreat retreat Fig. 2. Commander as traitor

6 Assumptions A1. Every message is delivered correctly A2. Receiver knows the sender A3. Failure can be detected

7 Majority Rule 1.Choose the majority value, if exists Else Retreat 2. IF from an ordered set, choose the Median

8 Algorithm OM(0) 1)C : sends value to all L i 2)L i : IF receives, use value received ELSE Retreat OM(m), m > 0 1)C : sends value to all L i 2)L i : IF receives, use v i ELSE Retreat Enter OM(m - 1) as commander for (n - 2) L’s 3)FOR each i, and each j  i L j : IF receives, use v j ELSE Retreat L i : use majority (v 1, …., v n-1 )

9 Demo: OM(1), L3 as traitor C L1L2L3 a a a aaa a ? ? L2L3L1L3L1L2 OM(1) OM(0) L 1 said C said ‘a’ C said ‘a’ L 3 said C said ‘?’ Result : Majority (a, a, ?) = a

10 Demo: OM(1), ‘C’ as traitor C L1L2L3 a r a aar r a a L2L3L1L3L1L2 OM(1) OM(0) L 1 said C said ‘a’ C said ‘r’ L 3 said C said ‘a’ L 2 Result : Majority (a, r, a) = a; L1 C said ‘a’ L2 said C said ‘r’ L 3 said C said ‘a’ L 1 : Majority (a, r, a) = a

11 Image Credit: THANK YOU! ??Questions??


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