Multiprocessor Synchronization Algorithms (20225241) Lecturer: Danny Hendler

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!!!

Adminstrative details Office: Alon 218 Office hours: Wednesdays, 11-13 Or schedule an appointment Course site: http://www.cs.bgu.ac.il/~msa171/ (or simply access through my home page)

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: http://www.faculty.idc.ac.il/gadi/book.htm

5

Moore’s law Exponential growth in computing power 6 6

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

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

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

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

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

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

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

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?

Motivating examples of Synchronization

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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