Termination Detection

1. Termination Detection • definition • motivation for termination detection • main concepts in termination • termination announcement • termination detection • Dijkstra-Scholten termination detection for diffusing comptuations • Shavit-Francez generalization • wave-based • snapshot and weight-throwing-based

2. Definitions • terminal state (fixpoint) – no actions enabled • terminal state of process – a special local state of a process where no event of the process is applicable • deadlock is an example of terminal state • termination • implicit (message termination) - state that allows the receipt of messages but there are no messages in the channels - no action can be executed but the processes are not aware of termination • explicit (process termination) - a terminal state with every process in terminal state and no messages in channels • implicit termination is easier to design since the processes do not need to know the algorithm terminated

3. Why Termination Detection • objective - convert message terminating algorithms into process terminating. • achieved by adding two additional algorithms. The original algorithm is called basic algorithm. The added algorithms perform two tasks: • termination detection – recognize that the basic algorithm is in message terminating state • termination announcement – makes all processes go into designated terminating state • the added algorithms may exchange messages. They are called control messages

4. More Definitions • event can be internal or external (receipt of message) • each basic process is assumed to be in one of two states: • active - an action of the process is enabled (able to execute) • passive - no process actions are enabled • variable statep represents whether process is active or passive • the following assumptions about basic algorithms: • active process becomes passive only on internal event • process always becomes active when a message is received • internal events where process becomes passive are the only internal events (we ignore active  active events) • diffusing computation (centralized algorithm)- algorithm where only one process is active in every initial state • this process is called initiator

5. Termination Announcement • To announce terminationstop control messageis flooded to all processes • each process sendsstop message toevery neighbor • messages are sent at most once: • on local call to Announce • on receiving the first stop • the algorithm terminates when it receives stop from every neighbor • the algorithm works on directed and undirected networks, requires no identities, leader or topological knowledge • what does this algorithm resemble? • what happens when multiple nodes call announce simultaneously?

6. Dijkstra-Scholten Termination Detection • The algorithm works on diffusing computations only, p0 is initiator • the algorithm dynamically maintains a computation tree T=(VT,ET) • Either T is empty, or T is a directed tree with root p0 • VT includes all active processes and all basic messages in transit • initiator calls Announce when p0 VT (which implies that T is empty) • when process p sends basic message mes it becomes the father of this message • when mes is received by q • if q is involved in computation (does not have a father) it set p to be its father • q has a father it sends message sig back to p • each process p maintains variable scp that counts the number of sons • every time p sends mes, scp is incremented • every time p receives sig it is decremented • when scp is 0 and p is passive, it sends sig to its parent

7. Termi-nation detection Sp - basic sendRp - basic receiveIp - change from active to passiveAp - arrival of signal

8. Shavit-Francez Generalization to the Decentralized Algorithm • Dijkstra-Scholten algorithm works only on diffusing computations (one initiator) • Shavit-Francez suggested generalization to decentralized algorithms (multiple initiators) • in their algorithm each initiator maintains a computation tree similar to Dijkstra-Scholten • problem - when the tree on one initiator collapsed the initiator does not know if the computation terminated - there still may be other trees • solution - all processes participate in a wave • non-initiator process continues the wave • initiator process continues the wave only if its tree has collapsed • by definition of wave a process decides only when all system processes made at least one move. Thus when one process decides the basic computation terminates. • when process decides - it calls Announce

9. Termination Detection UsingSnapshots and Weight Throwing • snapshots • when process becomes passive it initiates a snapshot • if an active process receives a snapshot message, it ignores it • eventually, a snapshot succeeds, if this snapshot does not have messages in transition  detect termination • if a snapshot succeeds, does it mean that the basic alg. terminated? • weight throwing • each active process starts with a certain quantity (weight). The sum of all weights is 1. • when a process sends a message it sends part of its weight with it, when message arrives, the process adds the message’s weight to its own • when a process becomes passive, it sends its weight to initiator • when initiator’s weight is equal to 1, detect termination