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Termination Detection Algorithm for Distributed Computations Edsger W. Dijkstra W.H.J. Feijen A.J.M. van Gasteren Presented by : Charu Jain

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Presentation and Derivation of the Algorithm System Description System Description N machines N machines Active or Passive Active or Passive Stable State Stable State

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Initiation Machine nr.0 initiates the “probe” Machine nr.0 initiates the “probe” Ring-Minimize the signaling traffic Ring-Minimize the signaling traffic Assumption about passivity Assumption about passivity

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Propagation Propagation of the probe Propagation of the probe System State - P System State - P Probe ends with t=0 Probe ends with t=0

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Stipulation for concluding termination Termination Termination Invariant Invariant t=0 t=0 Info at nr.0 Info at nr.0 Invariant has to hold independent of the distribution of the activity Invariant has to hold independent of the distribution of the activity

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Absence of Messages P0 : (A i: t*
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Presence of Messages P0 is falsified -> Weaker invariant P0 V P1 P0 is falsified -> Weaker invariant P0 V P1 P1: (E j: 0<=j<=t : machine nr.j is black) P1: (E j: 0<=j<=t : machine nr.j is black) A machine sending a message to a machine with a number higher than it’s own makes itself Black A machine sending a message to a machine with a number higher than it’s own makes itself Black Termination Detection Termination Detection (t=0^machine nr.0 is white) => ~P1 (t=0^machine nr.0 is white) => ~P1

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Continued… P1 may be falsified and hence invariant P0 V P1 – Weaker invariant P0 V P1 V P2 P1 may be falsified and hence invariant P0 V P1 – Weaker invariant P0 V P1 V P2 P2 : the token is black P2 : the token is black nr. i+1 hands over a black token to nr. i if it itself is black nr. i+1 hands over a black token to nr. i if it itself is black Termination detection Termination detection Token is white => ~P2 Token is white => ~P2

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Unsuccessful Probe A black token at nr. 0 or a black nr. 0 A black token at nr. 0 or a black nr. 0 Next probe Next probe nr. 0 makes itself white and sends a white token to nr. N-1 nr. 0 makes itself white and sends a white token to nr. N-1 Upon transmission of the token to nr. i machine nr. i+1 becomes white (P1 is not falsified) Upon transmission of the token to nr. i machine nr. i+1 becomes white (P1 is not falsified)

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Termination A probe initiated after termination will end up with all machines white, and, hence a next probe is guaranteed to return a white token to a white machine nr.0. A probe initiated after termination will end up with all machines white, and, hence a next probe is guaranteed to return a white token to a white machine nr.0. Simplified rule – A machine sending a message makes itself black. Simplified rule – A machine sending a message makes itself black. Assumption of instantaneous messaging. Assumption of instantaneous messaging.

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