1. CIS 720
Mutual Exclusion 2

2. Tie Breaker Algorithm in1 = false; in2 = false; last = 1 co 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

3. Barrier synchronization
Worker[i]: do
true 
code for task i
wait for all tasks to complete od

4. Barrier synchronization
Worker[i]: do
true 
code for task i
<count = count + 1>
< await( count == n) > od

5. Barrier synchronization
Worker[i]: do
true 
code for task i
<count = count + 1>
< await( count == n) > od

6. Barrier synchronizationco
worker[i]: Coordinator
do true  do true 
code for task i for (i = 1 to n)
arrive[i] = await(arrive[i]= 1);
await(continue ==1) continue = 1
od od oc

7. Barrier synchronizationco
worker[i]: Coordinator
do true  do true 
code for task I; for (i = 1 to n)
arrive[i] = { await(arrive[i]= 1);
await(continue[i]==1) arrive[i] = 0; }
continue[i] = 0; for (i = 1 to n) continue[i] = 1
od od oc
Flag rule: A process that waits for the synchronization flags should reset it.

8. Invariant based approach
Identify synchronization regions in your program
Synchronization region: segment of code or control point at which a thread must wait for another thread or signal another thread.

9. Mutual exclusion CS1 CS2 do (true) do (true) 
****start of region **** start of region
critical section critical section
**** end of region **** end of region
non-critical section non-critical section od

10. Mutual exclusion CS1 CS2 Associate in and out counter with each region
do (true) do (true) 
****start of region **** start of region
in1 = in in2 = in2 + 1
critical section critical section
**** end of region **** end of region
out1 = out1+1; out2 = out2+1;
non-critical section non-critical section od
Associate in and out counter with each region

11. Mutual exclusion CS1 CS2 Associate in and out counter with each region
do (true) do (true) 
****start of region **** start of region
in1 = in in2 = in2 + 1
critical section critical section
**** end of region **** end of region
out1 = out1+1; out2 = out2+1;
non-critical section non-critical section od
Associate in and out counter with each region
Write an invariant using in and out counters
I = (in1=out1) \/ (in2=out2)

12. Mutual exclusion CS1 CS2 do (true) do (true) 
****start of region **** start of region
<await(in2=out2) in1 = in1 + 1> <await(in1=out1) in2 = in2 + 1>
critical section critical section
**** end of region **** end of region
out1 = out1+1; out2 = out2+1;
non-critical section non-critical section od
Associate in and out counter with each region
Write an invariant using in and out counters
I = (in1=out1) \/ (in2=out2)
Derive guards for the increment assertions

13. Barrier Synchronization
P1 P2
do (true) do (true) 
task for p1 task for p2
****start of region **** start of region
**** end of region **** end of region od

14. Barrier CS1 CS2 Associate counters with each region
do (true) do (true) 
task for p1 task for p2
****start of region **** start of region
arrive1 = arrive arrive2 = arrive2 + 1
**** end of region **** end of region
depart1 = depart1+1; depart2 = depart2+1; od
Associate counters with each region

15. Barrier CS1 CS2 Associate counters with each region
do (true) do (true) 
task for p1 task for p2
****start of region **** start of region
arrive1 = arrive arrive2 = arrive2 + 1
**** end of region **** end of region
depart1 = depart1+1; depart2 = depart2+1; od
Associate counters with each region
Write an invariant using the counters
(depart[1] <= arrive[2]) /\ (depart[2] <= arrive[1])

16. Semaphores Two operations: P(s), V(s) Semaphore invariant:
nP = number of P operations invoked so far
nV = number of V operations invoked so far
init = initial value of s
nP <= nV + init

17. Binary semaphore: 0 <= s <= 1
Let s = nV + init – nP
Invariant: s >= 0
P(s): nP = nP + 1
<await s > 0  s = s - 1>
V(s): nV = nV + 1
< s = s + 1>
Binary semaphore: 0 <= s <= 1

18. Mutual exclusion CSi do (true)
in[i] = 1
critical section
in[i] = 0
non-critical section od
I = ( 0 <= (in[1] + in[2] + …. + in[n]) <= 1 )
Let mutex = 1 - (in[1] + in[2] + …. + in[n])
I = ( 0 <= mutex <= 1 )

19. Mutual exclusion CSi do (true)
critical section
non-critical section od
I = ( 0 <= (in[1] + in[2] + …. + in[n]) <= 1 )
Let mutex = 1 - (in[1] + in[2] + …. + in[n])
I = ( 0 <= mutex <= 1 )

20. Barrier CS1 CS2 do (true) do (true)  task for p1 task for p2
****start of region **** start of region
arrive1 = arrive arrive2 = arrive2 + 1
**** end of region **** end of region
depart1 = depart1+1; depart2 = depart2+1; od
Barrier1 = (arrive1 – depart2)
Barrier2 = (arrive2 – depart1)

21. Barrier CS1 CS2 Barrier1 = (arrive1 – depart2)
do (true) do (true) 
task for p1 task for p2
barrier barrier2++
barrier2--; barrier1--; od
Barrier1 = (arrive1 – depart2)
Barrier2 = (arrive2 – depart1)