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

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

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

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

Termination Announcement

To announce terminationstop 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?

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

Termi-nation

detection

Sp - basic sendRp - basic receiveIp - change from active to passiveAp - arrival of signal

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

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