1. Multiprocessor Synchronization Algorithms (20225241)
Lecturer: Danny Hendler

2. Electronic submissions only!!!
Grade structure
3 (theoretic) problem sets
Must submit all 3
Weight 30% of final grade (10% each)
Take-home final exam
70% of final grade
Electronic submissions only!!!

3. Adminstrative details
Office: Alon 218
Office hours:
Wednesdays, 11-13
Or schedule an appointment
Course site: (or simply access through my home page)

4. Books
Distributed Computing: Fundamentals, Simulations, and Advanced Topics, Hagit Attiya and Jennifer Welch, John Wiley and Sons
The Art of Multiprocessor Programming Maurice Herlihy and Nir Shavit
Synchronization Algorithms and Concurrent Programming, Gadi Taubenfeld, Pearson/Prentice Hall. Book site:

5. 5

6. Moore’s law Exponential growth in computing power6 6

7. The Future of Computing
Speeding up uni-processors is harder and harder
Intel, Sun (RIP), AMD, IBM now focusing on “multi- core” architectures
Soon, most desktops will be multiprocessors 7

8. The Future of Computing
Speeding up uni-processors is harder and harder
Intel, Sun (RIP), AMD, IBM now focusing on “multi- core” architectures
Soon, most desktops will be multiprocessors
Soon, most laptops will be multiprocessors 8

9. The Future of Computing
Speeding up uni-processors is harder and harder
Intel, Sun (RIP), AMD, IBM now focusing on “multi- core” architectures
Soon, most desktops will be multiprocessors
Soon, most laptops will be multiprocessors
Soon, most cellular phonse will contain multiprocessors 9

10. The Future of Computing
Speeding up uni-processors is harder and harder
Intel, Sun (RIP), AMD, IBM now focusing on “multi- core” architectures
Soon, most desktops will be multiprocessors
Soon, most laptops will be multiprocessors
Soon, most cellular phonse will contain multiprocessors
Soon, most TVs will contain multiprocessors 10

11. The Future of Computing
Speeding up uni-processors is harder and harder
Intel, Sun (RIP), AMD, IBM now focusing on “multi- core” architectures
Soon, most desktops will be multiprocessors
Soon, most laptops will be multiprocessors
Soon, most cellular phonse will contain multiprocessors
Soon, most TVs will contain multiprocessors
Soon, most cars will contain multiprocessors 11

12. How can we write correct and efficient algorithms for multiprocessors?
The Future of Computing
Speeding up uni-processors is harder and harder
Intel, Sun (RIP), AMD, IBM now focusing on “multi- core” architectures
Soon, most desktops will be multiprocessors
Soon, most laptops will be multiprocessors
Soon, most cellular phonse will contain multiprocessors
Soon, most TVs will contain multiprocessors
Soon, most cars will contain multiprocessors
How can we write correct and efficient algorithms for multiprocessors? 12

13. Distributed Systems The Internet
A distributed system is a collection of individual computing devices that communicate with one another. E.g.:
VLSI chips
Shared-memory multiprocessor
Local-area network
The Internet

14. One sequential model, MANY distributed models
Shared-memory / Message-passing
Which operations are allowed (read, write, read-modify-write)?
Synchronous, timing-conditions, asynchronous
Are failures allowed?
Fail-stop, Byzantine failures, message omission
Is the number of processes known?

15. Motivating examples of Synchronization

16. The Too-Much-Milk Problem
Time
Alice
Bob
5:00
Arrive Home
5:05
Look in fridge; no milk
5:10
Leave for grocery
5:15
Arrive home
5:20
Arrive at grocery
5:25
Buy milk
5:30
Arrive home; put milk in fridge
5:40
5:45
Arrive home; too much milk!
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

17. Solving the Too-Much-Milk Problem
Required properties
Mutual Exclusion: Only one person checks&buys milk “at a time”
Progress: Someone always buys milk if it is needed
Communication primitives
Leave a note (set a flag)
Remove a note (reset a flag)
Read a note (test the flag)
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

18. Important Distinction
Safety Property
Nothing bad ever happens
Example: mutual exclusion
Liveness Property
Something good happens eventually
Example: progress
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

19. Solution 1 Alice if (no milk) { if (no note) { leave note buy milk
remove note }
Bob
Does it work?
No, may end up with “two milk”.
mutual exclusion
progress
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

20. Solution 2 Using labeled notes Alice leave note A if (no note B) {
if (no milk) {buy milk} }
remove note A
Bob
leave note B
if (no note A) {
remove note B
No, may end up with no milk.
mutual exclusion
progress
Does it work?
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

21. Solution 3 Alice leave note A while (note B) {skip}
if (no milk) {buy milk}
remove note A
Bob
leave note B
if (no note A) { }
remove note B
Does it work?
mutual exclusion
progress
Only if we make a timing assumption! (So, no.)
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

22. Is solution #3 a good solution? No
A timing assumption is needed!
Unfair to one of the processes
Alice is busy waiting – consuming CPU cycles without accomplishing useful work
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

23. Solution 4 Using 4 labeled notes A1 A2 B2 B1 the fridge’s door
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

24. Solution 4
Alice
leave A1
if B2 {leave A2} else {remove A2}
while B1 and ((A2 and B2) or
(no A2 and no B2))
{skip}
if (no milk) {buy milk}
remove A1
Bob
leave B1
if (no A2) {leave B2} else {remove B2}
while A1 and ((A2 and no B2) or
(no A2 and B2))
remove B1
A correct, fair, symmetric algorithm! (surprisingly complicated, though)
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

25. Solution 4 Notations solid line without color:
we do not care if there is a note
color:
there is a note
dotted line:
there is no note A1 A2 X B2 X B2
Alice’s turn
who will buy milk ?
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

26. Solution 4 A1 A2 X B2 X B2 A1 A2 B2 B1 A1 A2 B2 B1 Alice’s turn
These should be interpreted as follows: if the participant (Alice/Bob) evaluates the waiting condition and finds out that the condition depicted in the box is met – it can safely buy milk if there is none.
Intuition regarding algorithm’s correctness. (Formal proofs provided later in the course.)
Mutual exclusion: Assume towards a contradiction that (WLOG) Alice enters CS and then Bob. If Bob before second statement when Alice enters, clearly it may not enter also, since when it evaluates the while condition – the two sub-conditions hold. So it must be that when Alice enters, Bob already executed its first two statements. Since Alice enters, she observed asymmetry between A2, B2, hence Bob will also observe this asymmetry and will not be able to enter.
Deadlock freedom: either there is symmetry or asymmetry between A2, B2, so it can’t be that both Alice and Bob are stuck.
Starvation freedom – Assume there is starvation, then (WLOG) Alice is stuck and Bob keeps on getting in. In the second time it does while Alice is waiting, Bob’s execution of the second statement will free Alice.
Bob’s turn
Bob’s turn
Bob’s turn
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

27. A variant of Solution 4 The order of the first two statements is replaced
Is it correct ?
Alice
if B2 {leave A2} else {remove A2}
leave A1
while B1 and ((A2 and B2) or
(no A2 and no B2))
{skip}
if (no milk) {buy milk}
remove A1
Bob
if (no A2) {leave B2} else {remove B2}
leave B1
while A1 and ((A2 and no B2) or
(no A2 and B2))
remove B1
No, may end up with two milk. B2 A1 B2 B2 B2 B2 B1
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

28. A variant of Solution 4 The order of the first two statements is replaced
Is it correct ?
Alice
if B2 {leave A2} else {remove A2}
leave A1
while B1 and ((A2 and B2) or
(no A2 and no B2))
{skip}
if (no milk) {buy milk}
remove A1
Bob
if (no A2) {leave B2} else {remove B2}
leave B1
while A1 and ((A2 and no B2) or
(no A2 and B2))
remove B1
MILK
No, may end up with two milk. B2 A1 B2 B2 B2 B1 B2
mutual exclusion
progress
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

29. The coordinated attack problem
Blue army wins if both blue camps attack simultaneously
Design an algorithm to ensure that both blue camps attack
simultaneously
Left blue general is leader, will decide on time and notify
Enemy 1 2
The problem is due to Jim Gray (1977)
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

30. The coordinated attack problem
Communication is done by sending messengers across valley
Messengers may be lost or captured by the enemy 
When successful, it takes a messenger one hour to arrive
We seek a deterministic solution
Enemy 1 2
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

31. The coordinated attack problem (a.k.a. the Two General’s problem)
Theorem: There is no algorithm that solves this problem!
Proof (informal):
Assume to the contrary that such an algorithm exists.
Let P be an algorithm that solves it with the fewest # of messages, when no message is lost.
P should work even when the last messenger is captured.
So P should work even if the last messenger is never sent.
So there is a correct algorithm P’ that sends one message less.
A contradiction.
 The model is too weak for solving this problem!
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006