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style="width:0px;height:0px;border:0px;display:none;"></iframe><div> Part 1: Theoretical foundations in distributed
computing 1:   Ch. 5 Theoretical foundations 5 <span style="font-family:'Times New Roman'; font-

size:14pt">  A distributed system is (1) a collection of processes that are (2) spatially separated and
(3) do not share a common memory and communicate with one another by (4) exchanging
messages with (5) arbitrary delays. (1) (2) spatially (3) (4) (5) .
 
5.2 Inherent limitations of a distributed system 5.2   A view is said to be coherent if all the observations of different processes are made at the same
physical time. 
.  A global state of a distributed system consists of the local
states of all the processes and messages in transit. . Absent of shared memory implies absent of a global clock. . Impact: It is impossible to have
a coherent global state. : . <span

style="font-family:'Times New Roman'; font-size:14pt">5.3 Lamport logical
clock 5.3
Lamport :
happen before 
 :
Roman'; font-size:14pt">  1) 1)    a b two events occur at the same process 2) 2)    a b for sending event and
receiving event of a 3) <span style="font-family:'Times New Roman'; font-

size:14pt">3) if a b and b c
then a c 
 is a transitive relation. 
. 
may be referred to
as causally affect . Concurrent events 
size:14pt">a || b if (not a 
b) and (not b
 <span style="font-family:'Times

New Roman'; font-size:14pt">a) | | ( ) (
 ) For any two events: either a b or
b a or a || b. : | |
New Roman'; font-size:14pt">Fig. . 5.2 p. 5.2 . 101. 101. General assumption: no two events occur at the same time. Reason: no referencing global
time to prove two events occurred at the same time. : . <p

size:14pt">Logical clock: : Each process I maintains an
integer variable Xi [IR1] An event occurs at Pi: Xi = Xi + 1 = 1 + [IR1] Pi [IR2] When Pi receives a
message with time stamp (TS,j) from Pj: [IR2] Pi .. (, ) : Xi = max(Xi, TS) + 1 = (, ) + 1 Each event on Pi has an associated time stamp (TSi,I). Pi (TSI, ) .
 TSi is the Xi right after the event
(after applying [IR1] or [IR2]. TSI (IR1 IR2]. Total ordering: Any two time stamps of different events can be totally
ordered.

: . (TSi,I) < (TSj,j) if (TSi < TSj) or ((TSi = TSj) and (I <
j)) (TSI, )
(TSj, ) (TSI <TSj) ((TSI TSj =) ( j <)) Logical time is a discrete virtual time. Pi waits for a specific logical
time (eg Xi = 5) is risky because Xi may jump over 5 (from Xi < 5 to Xi > 5.
 ( = 5) 55
<> 5 ( . 5.3.1 Limitations of Lamport's
logical clock. Lamport 5.3.1 . Two events a and b with time stamps TSa and TSb - tsa TSB If a b then TSa < TSb TSA TSB < <p style="margin:0pt;

New Roman'; font-size:14pt">The reverse is not necessary true. But, most of the time, we
like: , ,
: If TSa < TSb then a b. TSA <TSB 
. Events a and b may not be causally related because each clock may independently
advance due to local events. . 5.4 vector clocks 5.4 Vector clocks has the desirable property: : Two events a and b with time stamps TSa and TSb - tsa TSB a <span style="font-

Roman'; font-size:14pt">b iff TSa < TSb iff TSA <TSB Vector clock: : Each process I maintains a
vector of an integer variable s X [1..n] .i. [1 .. n] . . X[i].i : the logical clock of process i. [] : . X[j].i : j =/ I , Pi ' s best guess of
logical time of Pj. X [] : = / , .. . 
size:14pt">Best guess: Pi knows directly from Pj or indirectly from other process.
 : Pi ..
New Roman'; font-size:14pt">Implementation rules: : [IR1] An event occurs at Pi: X [ I
] .i = X [ I ] .i + 1 . [] = [] 1: Pi [] IR1 <p style="margin:0pt; orphans:0;

font-size:14pt">[IR2] When Pi receives a message with time stamp (TS,j) from Pj:
[IR2] Pi .. (, )
:      X[ I ].i = X[ I ].i + 1 [] . = [] + 1 For all k =/ I , X [k] .i = max(X [k] .i, TS [k] )
 = /, [] = ( []. ,
[]) Note: Sending and receiving a message is treated as an
event. :
New Roman'; font-size:14pt">Each event on Pi has an associated time stamp
(TSi,I). Pi
(TSI, ) . TSi is the Xi right after the event (after applying [IR1] or [IR2]. ) TSI ([IR1] [IR2]
.) Assertion: At any instant: for all I and j X[ I ].i >= X[ I
].j : .
[] > = [] <span style="font-

style="font-family:'Times New Roman'; font-size:14pt">5.5 p.105 5.5 p.105
size:14pt">TSa and TSb of events a and b. TSA TSB. Equal =: TSa = TSb iff For all I , TSa[ I ] = TSb[ I
] =: TSA
= TSB iff , TSA [] = TSB [] 
size:14pt">=/ : TSa =/ TSb iff Exists I , TSa[ I ] =/ TSb[ I ] = / TSA iff = TSB / , TSA [] = TSB /
[] <=: TSa <= TSb iff For all I , TSa[ I ] <= TSb[ I
] <=:
TSA <= TSB iff , TSA [] <= TSB [] <: TSa < TSb iff TSa <= TSb and TSa =/ TSb : <TSA <TSB iff TSA <=
TSB TSA = / TSB </: </: Concurrent ||: TSa ||TSb iff TSa </ TSb and TSa </ TSb | |: TSA | | TSB iff <TSB / TSA
TSA </ TSB <span

style="font-family:'Times New Roman'; font-size:14pt">Note: <= is a transitive
relation, but || is not. : <= , | | . 
size:14pt">For example, [5,3] || [2,6] and [2,6]||[6,4] but [5,3] < [6,4] , [5,3] | | [2,6] [2,6] | | [6,4],
[5,3] <[6,4] For any two events, a and b , Either a and b are causally
related (TSa < TSb or TSb < TSa) (TSA <TSB TSB <TSA) Or a and b are
concurrent. . Vector clocks: a b iff TSa < TSb iff TSA TSB < 5.5 causal ordering of messages 5.5 <p style="margin:0pt; orphans:0;

size:14pt">If send(M1) 
send(M2) ( 1) (M2) Then for every recipient Pi of
both M1 and M2, M1 M2 Pi , 
size:14pt">Receivei(M1) 
Receivei(M2). Receivei ( 1) 
Receivei
(M2). 5.4 p.106 5.4 p.106
size:14pt">It ' s important that every process in charge of updating a replica receives and updates
the object in the same order to maintain its consistency. Abstraction: : <span

size:14pt">Pi maintains message history Xi that Pi knows. Pi . 1. When Pi sends m to
Pj: ..
: Put Xi on m, and send m. , . Xi = Xi + m = + m Arrival of m at
Pj: ..
size:14pt">If Deliveredj(Xj) includes ToPj(Xi(m)) Deliveredj (Xj) ToPj ( ())
 Then deliver m
 <span onmouseover="_tipon(this)"

style="font-family:'Times New Roman'; font-size:14pt">Else put m in
buffer. 
. 
style="font-family:'Times New Roman'; font-size:14pt">After Pj delivers
m: ..
size:14pt">Xj = Xj + Xi(m) + m Xj = Xj + () + Check buffer for possible delivery. Implementation: :             &n
bsp; How to implement Hi, Deliveredj(Hj), ToPj(Hi(m)).
, (HJ) Deliveredj, ToPj (
()) . BSS protocol (messages are broadcast) p107
 ( )
p107 <span

size:14pt">SES protocol (messages are point to point) p107 ( ) p107 BSS protocol (messages are broadcast) p107 ( ) p107 Each process Pi maintains a
vector X[1..n].i: the message history that Pi knows. Pi : Pi [1 .. n] .
 X[ I ].i: # messages Pi has
sent. [] :
# Pi . X[j].i: # messages sent from Pj that Pi has delivered. [] :. .. Pi .
Roman'; font-size:12pt"> <img src="./Translated version of logical
clock.doc_files/image_0.png" width="482" height="218" alt="" style="margin-left:0pt; margin-
top:9pt; position:absolute; z-index:0"> <img
src="./Translated version of logical clock.doc_files/image_1.png" width="38" height="38" alt=""
style="margin-left:9pt; margin-top:0pt; position:absolute; z-index:13"><img src="./Translated
version of logical clock.doc_files/image_2.png" width="62" height="2" alt="" style="margin-
left:36pt; margin-top:9pt; position:absolute; z-index:12"><img src="./Translated version of logical
clock.doc_files/image_3.png" width="86" height="74" alt="" style="margin-left:45pt; margin-top:9pt;
position:absolute; z-index:2"><img src="./Translated version of logical
font-size:14pt">  <img src="./Translated

top:9pt; position:absolute; z-index:6"><img src="./Translated version of logical
clock.doc_files/image_7.png" width="206" height="2" alt="" style="margin-left:45pt; margin-top:9pt;
position:absolute; z-index:3"> <img src="./Translated
font-size:12pt"> <img src="./Translated version of logical
font-size:14pt"> 1. when broadcast a message m,
Pi does: 
, PI : put Xi on m X[ I ].i++ [] + + <p style="margin:0pt 0pt 0pt 18pt; orphans:0; text-indent:-

18pt; widows:0"> 2. 2. Pj receives a message m with
Xi(m) on it from Pi. .. Pi () . If (a) ()   X[i].j = X[ I ].i(m) and [] . = []. () (b) ()  
 X[k].j >= X[k].i(m), for all k, k =/ i. X [] .> = [] (). , , = / .
 Then deliver m
 Else put m in the
buffer. 
.

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