CSE 480 Lecture Notes
February 22, 1996 


A distributed system consists of a finite set of processes and a finite set
of channels.

Global State

- Fig. 5-6 [SiSh94]
- global state diagram

n  = # of msgs sent by A along the channel before A's state was recorded
n' = # of msgs sent by A along the channel before the channel's state was recorded

A consistent global state requires:  n = n'

m  = # of msgs received along the channel before B's state was recorded
m' = # of msgs received along the channel by B before the channel's state was recorded

Similarly, m = m'

Since the number of msgs sent along the channel cannot be less than the
number of msgs received along that channel, we have n' >= m. 
Thus, n >= m for a consistent global state.

Def. LSi is the local state of site Si.
  1. values of local variables
  2. seq of msgs sent or received

Note: Site Si could be process Pi.

The global state of a distributed computation is n-tuples
of local states; i.e., GS = (LS1,LS2,...,LSn).

- send(Mij): the send event of msg Mij from Pi to Pj
- recv(Mij): the receive event of msg Mij by Pj
- time(x): the time at which state x was recorded; time(send(m)) denote
the time at which event send(m) occurred.

For local states LSi and LSj,
- transit(LSi,LSj) = {Mij | send(Mij) in LSi and recv(Mij) not_in LSj}
- inconsistent(LSi,LSj) = {Mij | send(Mij) not_in LSi and recv(Mij) in LSj}

A global state GS = (LS1,LS2,...,LSn) is consistent if
  for all i, j : inconsistent(LSi,LSj) = \emtpyset

A global state GS = (LS1,LS2,...,LSn) is transitless if
  for all i, j : transit(LSi,LSj) = \emtpyset

A global state is strongly consistent if it is consistent and transitless.

- Fig. 5-8 [SiSh94]
  {LS12,LS23,LS33} consistent
  {LS11,LS22,LS32} inconsistent
  {LS11,LS21,LS31} is strongly consistent

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Distributed Snapshots

Goal: to capture a consistent global state.

Ex: global snapshots of Penn campus or nature.
used in debugging

- Assume that communication channels are FIFO.
- To determine a global state, a process needs cooperation from other processes.
- The algorithm is to be superimposed on the underlying computation: it must
run concurrently with, but not alter the underlying computation.

- A process can record its own state and the msgs it sends and receives,
but nothing else.
- The state of a channel is the sequence of msgs sent along the channel,
excluding the msgs received along the channel.

Figures from [ChLa85]
Fig 1-4

The Algorithm:

- Marker-Sending Rule for a Process P.

- Marker-Receiving Rule for a Process Q.

Fig 8.
- Assume P records in S0, i.e., A
- P sends a marker along c
- The system moves to S1, S2 and then S3 while the marker in transit
- Q receives the marker in S3
- Q records its state, D, and c empty
- Q sends the marder along c'
- P receives it on c' and records <M'>
- the recorded global state is Fig 8

How to collect and assemble the recorded information?

Properties of the recorded global state

- may not correspond to a global state that actually occured.

Stable Property of a distribute system D

-Let y be a predicate function defined on the global state of a distributed system D;
that is, y(S) is true or false for a global state S of D.
- The predicate y is said to be a stable property of D if y(S) implies y(S')
for all global states S' of D reachable from the global state S of D.
I.e., Once it holds, it holds true for all later points in that computation.
- Examples: "computation has terminiated", "the system is deadlocked",
"all tokens in a token righ have disappeared"

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The local histrory of Pi is a (possibly infinite) seq of events
  h_i = e_i^1, e_i^2, ...

Let h_i^k = e_i^1, e_i^2, ..., e_i^k
  h_i^0 = empty seq

The global history of the computation is a set
  H = h_1 U ... U h_n

The notion of a CUT captures a global state in a distributed computation.

Def. A cut of a distributed comuptation is a set C = {c1,c2, ..., cn},
where ci is the cut event at site Si, i.e., local state LSi at that time.

Def. Let ek denote an event at site Sk.  A cut C = {c1,c2, ..., cn} is
a consistent cut if
  for all Si,Sj, there is no ei, ej such that
    (ei --> ej) and (ej --> cj) and (ei -/-> ci)
where ci,cj in C.

- A cut is consistent if every msg that was received before a cut event
was sent before the cut event at the sender site in the cut.

Fig. 5-10.

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Termination Detection

- A process active or idle
- A distributed computation is terminated iff all the processes
are idle and there are no msgs in transit.

Huang's Termination Detection Algorithm

- based on weight
- use controlling agent