CIS 720

Mutual Exclusion

Critical Section problem

• Process ido (true)

entry protocol;

critical section;

exit protocol;

non-critical section

od

Correctness

• Mutual exclusion: at most one process at a time is executing its critical section

• Absence of deadlock: If two or more processes are trying to enter their critical section, at least one will succeed

• Absence of unnecessary delay: If a process is trying to enter its critical section and the other processes are executing their non-critical sections or have terminated then the first process is not prevented from entering its critical section.

• Eventual entry: A process that is attempting to enter its critical section will eventually succeed.

Invariant based approach

CS1 CS2do (true) do (true)

entry protocol; entry protocol;in1 = true in2 = true

critical section critical sectionexit protocol; exit protocol;

in1 = false in2 = false non-critical section non-critical sectionod

Invariant based approach

CS1 CS2do (true) do (true)

<await (!lock) lock = true> <await(!lock) lock = true> critical section critical section lock = false lock = false non-critical section non-critical sectionod

Test and set instruction

CS1 CS2do (true) do (true) while (TS(lock)) skip; while(TS(lock)); critical section critical section lock = false lock = false non-critical section non-critical sectionod

Implementing await statements

• CSenter

while (!B) { CSexit; CSenter }

S;

CSexit

Tie Breaker Algorithmin1 = false; in2 = false; last = 1co

CS1: CS2: do true do true int = true; last = 1; in2 = true; last = 2; while(in2 /\ last == 1); while(in1 /\ last == 2); critical section critical section in1 = false; in2 = false; non-critical section non-critical section od od

oc

Tie Breaker Algorithmin1 = false; in2 = false; last = 1co

CS1: CS2: do true do true last = 1; in1 = true; last = 2; in2 = true <await (!in2 \/ last == 2)>; <await (!in1 \/ last ==

1)>; critical section critical section in1 = false; in2 = false; non-critical section non-critical section od od

oc

Ticket Algorithmnext = 1; number = 1; turn[1..n]= [0…0];co

CSi: do true < turn[i] = number; number = number + 1 >

await( turn[i] ) == next critical section <next = next + 1> non-critical section od

oc

Invariant: next > 0 and for all i,

cs[i] in CS turn[i] == next /\ turn[i] != turn[j] for all j

Bakery algorithm

turn1 = 0; turn2 = 0;co

CS1: CS2: do true do true turn1 = turn2 + 1; turn2 = turn1 + 1 while(turn2 != 0 /\ turn1 > turn2); while(turn1 != 0 and /\ turn2 > turn1);

critical section critical sectionturn1 = 0; turn2 = 0;non-critical section non-critical section

od odoc

Bakery algorithm

turn1 = 0; turn2 = 0;co

CS1: CS2: do true do true

turn = 1; turn2 = 1 turn1 = turn2 + 1; turn2 = turn1 + 1 while(turn2 != 0 /\ while(turn1 != 0 and /\

(turn1,1) > (turn2,2)); (turn2,2) > (turn1,1));critical section critical sectionturn1 = 0; turn2 = 0;non-critical section non-critical section

od odoc

Barrier synchronization

Worker[i]:

do

true

code for task i

wait for all tasks to complete

od

Barrier synchronization

Worker[i]:

do

true

code for task i

<count = count + 1>

< await( count == n) >

od

Barrier synchronization

Worker[i]:

do

true

code for task i

<count = count + 1>

< await( count == n) >

od

Barrier synchronization

coworker[i]: Coordinator do true do true code for task I; for (i = 1 to n) arrive[i] = 1 await(arrive[i]= 1);

await(continue ==1) continue = 1 od od

oc

Barrier synchronization

coworker[i]: Coordinator do true do true code for task I; for (i = 1 to n) arrive[i] = 1 { await(arrive[i]= 1);

await(continue[i]==1) arrive[i] = 0; } continue[i] = 0; for (i = 1 to n) continue[i] = 1

od odoc

Flag rule: A process that waits for the synchronization flags should reset it.