1. Termination Detection

2. Goal Study the development of a protocol for termination detection with the help of invariants.

3. Termination Detection Rules: –A process is either active or passive –An active process can become passive at any time –A passive process can become active only if it receives an computation message –Only active processes can send computation messages. All processes can receive them

4. A system is said to be terminated if –All processes are passive –No application messages are in transit We distinguish between computation messages and messages sent for detecting termination. Any process can send and receive them. These messages do not change the status of a process

5. Application A solution for termination detection allows one to ensure that all tasks in a system are indeed complete, even though the tasks may create additional tasks that are run at other processors in the system

6. Observation Termination detection is a stable property –Once true, it remains true forever Detecting such properties is important for many problems including –Garbage collection –Deadlock detection

7. We will consider two algorithms Based on the idea of diffusion Based on the idea of global snapshot –We will study these aspects later.

8. Approach 1: Dijkstra Scholten Assumptions –Initially one process is active –No failures, lost messages etc.

9. Each process j maintains a variable P.j that is its parent in the tree –At root, P.root = root –Initially for all other processes, P.j = NULL

10. Predicate in Invariant (1) The set of active processes form a tree –True in the initial state –Ensure that this remains true during computation

11. When a Process becomes active Consider the case when j changes from Passive to Active –It must be the case that j received a computation message from some process, say k P.j = k Become active

12. Action (1) P.j = NULL  j receives a message from k  P.j = k, j becomes active

13. When a Process Becomes Passive Consider the case when j changes from Active to Passive –It must be the case that j has no children

14. Action (2) P.j = NULL  j receives a message from k  P.j = k, j becomes active j is active  j wants to become passive  j has no children  j becomes passive, P.j = NULL

15. Problem? Does not deal with messages.

16. Predicate in Invariant (2) The set of active processes form a tree If j is passive then all messages it sent have been received –True initially –Preserve this predicate during computation

17. Action (3) Maintain a variable oc.j that denotes the number of messages that j has sent and are not yet acknowledged

18. Action (2) corrected P.j = NULL  j receives a message from k  P.j = k, j becomes active j is active  j wants to become passive  j has no children  oc.j = 0  j becomes passive, P.j = NULL

19. The actions on previous slide can be used to implement termination detection. Consider second action j is active  j wants to become passive  j has no children  oc.j = 0  j becomes passive, P.j = NULL Is it possible to drop ` j has no children’ from the guard?

20. Answer We could if we guarantee that –oc.j = 0  j has no children –Same as j has children  oc.j > 0 Could be achieved if the child does not respond to at least one of parent’s message (first one?) Thus, checking oc.j is 0 sufficient

21. Action (3) P.j = NULL  j receives a message from k  P.j = k, j becomes active (Don’t send ack to this message) j is active  j wants to become passive  j has no children  oc.j = 0  j becomes passive, P.j = NULL; send ack to parent j is active  j receives a message from k  Send ack to k Other simple actions for maintaining oc.j

22. Summarizing Approach 1 Goal –Active processes form a rooted tree If process k activates j then j sets its parent to k –If a process is passive, all messages it sent have been received Acknowledge each message (at some time) –A process becomes passive only when all its children are passive; in other words, force a process to wait for its children to become passive. This is achieved if the children do not send an acknowledgment for the first message received from the parent until they become passive.

23. Actions Passive  Active –If j is passive and receives a computation message from k then P.j = k Become active

24. Actions Active  Active –If j is active and receives a computation message from l Send an acknowledgment

25. Actions Message send –If j wants to send message (it must be active) oc.j ++ (Number of outstanding acknowledgments is increased) Acknowledgement receive –oc.j = oc.j – 1

26. Actions Active  passive –If j wants to be passive and oc.j = 0 Send an acknowledgment to P.j (Observe that the first message from parent was not immediately acknowledged) Become passive If j is the root then declare termination

27. Diffusing Computation Crucial for various applications General outline –root(?) sends the diffusion message –Every node that receives the diffusion message for the first time forwards it to its neighbors First node from which diffusion is received is called parent –All subsequent diffusion messages are acknowledged –Upon receiving acknowledgements form all neighbors, a node completes the diffusion and sends acknowledgment to parent –When root completes the diffusion, the diffusion computation is complete We will see application of diffusion computation later in the class.