Concurrent Objects Companion slides for The by Maurice Herlihy & Nir Shavit
Concurrent Computation memory object object 2
Objectivism What is a concurrent object? How do we describe one? How do we implement one? How do we tell if we re right? 3
Objectivism What is a concurrent object? How do we describe one? How do we tell if we re right? 4
FIFO Queue: Enqueue Method q.enq( ) 5
FIFO Queue: Dequeue Method q.deq()/ 6
A Lock-Based Queue class LockBasedQueue<T> { int head, tail; T[] items; Lock lock; public LockBasedQueue(int capacity) { head = 0; tail = 0; lock = new ReentrantLock(); items = (T[]) new Object[capacity]; } 7
A Lock-Based Queue head 0 1 capacity-1 class LockBasedQueue<T> { y z 2 int head, tail; T[] items; Lock lock; public LockBasedQueue(int capacity) { head = 0; tail = 0; lock = new ReentrantLock(); items = (T[]) new Object[capacity]; } tail Queue fields protected by single shared lock 8
A Lock-Based Queue head 0 1 capacity-1 class LockBasedQueue<T> { y z 2 int head, tail; T[] items; Lock lock; public LockBasedQueue(int capacity) { head = 0; tail = 0; lock = new ReentrantLock(); items = (T[]) new Object[capacity]; } Initially head = tail tail 9
Implementation: Deq head 0 1 public T deq() throws EmptyException capacity-1 { y z lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } } 2 tail 10
Implementation: Deq public T deq() throws EmptyException capacity-1 { y z lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } } finally { lock.unlock(); } head 0 1 Method calls mutually exclusive 2 tail 11
Implementation: Deq public T deq() throws EmptyException capacity-1 { y z lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } } finally { lock.unlock(); } head 0 1 If queue empty throw exception 2 tail 12
Implementation: Deq public T deq() throws EmptyException capacity-1 { y z lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } } finally { lock.unlock(); } head 0 1 Queue not empty: remove item and update head 2 tail 13
Implementation: Deq head 0 1 public T deq() throws EmptyException capacity-1 { y z lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } } Return result 2 tail 14
Implementation: Deq public T deq() throws EmptyException capacity-1 { y z lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; } head++; return x; } finally { lock.unlock(); } head 0 1 Release lock no matter what! 2 tail 15
Implementation: Deq public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } } 16
Now consider the following implementation The same thing without mutual exclusion For simplicity, only two threads One thread enq only The other deq only 17
Wait-free 2-Thread Queue public class WaitFreeQueue { int head = 0, tail = 0; items = (T[]) new Object[capacity]; public void enq(item x) { while (tail-head == capacity); // busy-wait items[tail % capacity] = x; tail++; } public Item deq() { while (tail == head); // busy-wait Item item = items[head % capacity]; head++; return item; }} 18
Wait-free 2-Thread Queue public class LockFreeQueue { int head = 0, tail = 0; items = (T[]) new Object[capacity]; head capacity-1 0 1 y z 2 tail public void enq(item x) { while (tail-head == capacity); // busy-wait items[tail % capacity] = x; tail++; } public Item deq() { while (tail == head); // busy-wait Item item = items[head % capacity]; head++; return item; }} 19
Lock-free 2-Thread Queue public class LockFreeQueue { int head = 0, tail = 0; items = (T[])new Object[capacity]; head capacity-1 0 1 y z 2 tail public void enq(item x) { while (tail-head == capacity); // busy-wait items[tail % capacity] = x; tail++; } public Item deq() { while (tail == head); // busy-wait Item item = items[head % capacity]; head+ +; return Queue item; is updated without a lock! }} 20
Defining concurrent queue implementations Need a way to specify a concurrent queue object Need a way to prove that an algorithm implements the object s specification Lets talk about object specifications 21
Correctness and Progress In a concurrent setting, we need to specify both the safety and the liveness properties of an object Need a way to define when an implementation is correct the conditions under which it guarantees progress Lets begin with correctness 22
Sequential Objects Each object has a state Usually given by a set of fields Queue example: sequence of items Each object has a set of methods Only way to manipulate state Queue example: enq and deq methods 23
Sequential Specifications If (precondition) the object is in such-and-such a state before you call the method, Then (postcondition) the method will return a particular value or throw a particular exception. and (postcondition, con t) the object will be in some other state when the method returns, 24
Pre and PostConditions for Dequeue Precondition: Queue is non-empty Postcondition: Returns first item in queue Postcondition: Removes first item in queue 25
Pre and PostConditions for Dequeue Precondition: Queue is empty Postcondition: Throws Empty exception Postcondition: Queue state unchanged 26
Why Sequential Specifications Totally Rock Interactions among methods captured by side-effects on object state State meaningful between method calls Documentation size linear in number of methods Each method described in isolation Can add new methods Without changing descriptions of old methods 27
What About Concurrent Specifications? Methods? Documentation? Adding new methods? 28
Methods Take Time time 29
Methods Take Time invocation 12:00 q.enq (...) time 30
Methods Take Time invocation 12:00 q.enq (...) Method call time 31
Methods Take Time invocation 12:00 q.enq (...) Method call time 32
Methods Take Time invocation 12:00 response 12:01 q.enq (...) void Method call time 33
Sequential vs Concurrent Sequential Methods take time? Who knew? Concurrent Method call is not an event Method call is an interval. 34
Concurrent Methods Take Overlapping Time time 35
Concurrent Methods Take Overlapping Time Method call time 36
Concurrent Methods Take Overlapping Time Method call Method call time 37
Concurrent Methods Take Overlapping Time Method call Method call Method call time 38
Sequential vs Concurrent Sequential: Object needs meaningful state only between method calls Concurrent Because method calls overlap, object might never be between method calls 39
Sequential vs Concurrent Sequential: Each method described in isolation Concurrent Must characterize all possible interactions with concurrent calls What if two enqs overlap? Two deqs? enq and deq? 40
Sequential vs Concurrent Sequential: Can add new methods without affecting older methods Concurrent: Everything can potentially interact with everything else 41
Sequential vs Concurrent Sequential: Can add new methods without affecting older methods Concurrent: Everything can potentially interact with everything else 42
The Big Question What does it mean for a concurrent object to be correct? What is a concurrent FIFO queue? FIFO means strict temporal order Concurrent means ambiguous temporal order 43
Intuitively public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } } 44
Intuitively public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } } finally { lock.unlock(); } All modifications of queue are done mutually exclusive 45
Intuitively Lets capture the idea of describing the concurrent via the sequential lock() q.deq unlock() q.enq deq lock() enq unlock() Behavior is Sequential time enq deq 46
Linearizability Each method should take effect Instantaneously Between invocation and response events Object is correct if this sequential behavior is correct Ordering must be maintained between request and responses (addendum) Any such concurrent object is Linearizable 47
Is it really about the object? Each method should take effect Instantaneously Between invocation and response events Sounds like a property of an execution A linearizable object: one all of whose possible executions are linearizable 48
Example time (6) 49
Example q.enq(x) time (6) 50
Example q.enq(x) q.enq(y) time (6) 51
Example q.enq(x) q.enq(y) q.deq(x) time (6) 52
Example q.enq(x) q.deq(y) q.enq(y) q.deq(x) time (6) 53
Example q.enq(x) q.deq(y) q.enq(y) q.deq(x) time (6) 54
Example q.enq(x) q.deq(y) q.enq(y) q.deq(x) time (6) 55
Example time (5) 56
Example q.enq(x) time (5) 57
Example q.enq(x) q.deq(y) time (5) 58
Example q.enq(x) q.deq(y) q.enq(y) time (5) 59
Example q.enq(x) q.deq(y) q.enq(y) time (5) 60
Example q.enq(x) q.deq(y) q.enq(y) time (5) 61
Example time (4) 62
Example q.enq(x) time (4) 63
Example q.enq(x) q.deq(x) time (4) 64
Example q.enq(x) q.deq(x) time (4) 65
Example q.enq(x) q.deq(x) time (4) 66
Example q.enq(x) time (8) 67
Example q.enq(x) q.enq(y) time (8) 68
Example q.enq(x) q.deq(y) q.enq(y) time (8) 69
Example q.enq(x) q.deq(y) q.enq(y) q.deq(x) time (8) 70
Example q.enq(x) q.deq(y) q.enq(y) q.deq(x) time 71
Read/Write Register Example write(0) read(1) write(2) write(1) read(0) time (4) 72
Read/Write Register Example write(0) read(1) write(2) write(1) already happened write(1) time read(0) (4) 73
Read/Write Register Example write(0) read(1) write(2) write(1) already happened write(1) time read(0) (4) 74
Read/Write Register Example write(0) read(1) write(2) write(1) already happened write(1) time read(0) (4) 75
Read/Write Register Example write(0) read(1) write(2) write(1) already happened write(1) time read(1) (4) 76
Read/Write Register Example write(0) read(1) write(2) write(1) already happened write(1) time read(1) (4) 77
Read/Write Register Example write(0) read(1) write(2) write(1) already happened write(1) time read(1) (4) 78
Read/Write Register Example write(0) write(2) write(1) read(1) time (4) 79
Read/Write Register Example write(0) write(2) write(1) read(1) time (4) 80
Read/Write Register Example write(0) write(2) write(1) read(1) time (4) 81
Read/Write Register Example write(0) read(1) write(2) write(1) read(1) time (2) 82
Read/Write Register Example write(0) read(1) write(2) write(1) read(1) time (2) 83
Read/Write Register Example write(0) read(1) write(2) write(1) read(1) time (2) 84
Read/Write Register Example write(0) read(1) write(2) write(1) read(2) time (2) 85
Talking About Executions Why? Can t we specify the linearization point of each operation without describing an execution? Not Always In some cases, linearization point depends on the execution 86
Formal Model of Executions Define precisely what we mean Ambiguity is bad when intuition is weak Allow reasoning 87
Split Method Calls into Two Events Invocation method name & args q.enq(x) Response result or exception q.enq(x) returns void q.deq() returns x q.deq() throws empty 88
Invocation Notation A q.enq(x) (4) 89
Invocation Notation A q.enq(x) thread (4) 90
Invocation Notation A q.enq(x) thread method (4) 91
Invocation Notation A q.enq(x) thread method object (4) 92
Invocation Notation A q.enq(x) thread method object arguments (4) 93
Response Notation A q: void (2) 94
Response Notation A q: void thread (2) 95
Response Notation A q: void thread result (2) 96
Response Notation A q: void thread result object (2) 97
Response Notation A q: void thread result object (2) 98
Response Notation A q: empty() thread exception object (2) 99
History - Describing an Execution H = A q.enq(3) A q:void A q.enq(5) B p.enq(4) B p:void B q.deq() B q:3 Sequence of invocations and responses 100
Definition Invocation & response match if Thread names agree A q.enq(3) A q:void Object names agree Method call (1) 101
Object Projections H = A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 102
Object Projections H q = A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 103
Thread Projections H = A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 104
Thread Projections H B = A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 105
Complete Subhistory H = A q.enq(3) A q:void A q.enq(5) B p.enq(4) B p:void B q.deq() An invocation is B q:3 pending if it has no matching respnse 106
Complete Subhistory H = A q.enq(3) A q:void A q.enq(5) B p.enq(4) B p:void B q.deq() B q:3 May or may not have taken effect 107
Complete Subhistory H = A q.enq(3) A q:void A q.enq(5) B p.enq(4) B p:void B q.deq() B q:3 discard pending invocations 108
Complete Subhistory A q.enq(3) A q:void Complete(H) = B p.enq(4) B p:void B q.deq() B q:3 109
Sequential Histories A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 A q:enq(5) (4) 110
Sequential Histories A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 A q:enq(5) match (4) 111
Sequential Histories A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 A q:enq(5) match match (4) 112
Sequential Histories A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 A q:enq(5) match match match (4) 113
Sequential Histories A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 A q:enq(5) (4) match match match Final pending invocation OK 114
Sequential Histories A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 A q:enq(5) (4) match match match Final pending invocation OK 115
Well-Formed Histories H= A q.enq(3) B p.enq(4) B p:void B q.deq() A q:void B q:3 116
Well-Formed Histories Per-thread projections sequential H= A q.enq(3) B p.enq(4) B p:void B q.deq() A q:void B q:3 H B= B p.enq(4) B p:void B q.deq() B q:3 117
Well-Formed Histories Per-thread projections sequential H= A q.enq(3) B p.enq(4) B p:void B q.deq() A q:void B q:3 H B= H A= B p.enq(4) B p:void B q.deq() B q:3 A q.enq(3) A q:void 118
Equivalent Histories Threads see the same thing in both H A = G A H B = G B H= A q.enq(3) B p.enq(4) B p:void B q.deq() A q:void B q:3 G= A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 119
Sequential Specifications A sequential specification is some way of telling whether a Single-thread, single-object history Is legal For example: Pre and post-conditions But plenty of other techniques exist 120
Legal Histories A sequential (multi-object) history H is legal if For every object x H x is in the sequential spec for x 121
Precedence A q.enq(3) B p.enq(4) B p.void A q:void B q.deq() B q:3 A method call precedes another if response event precedes invocation event Method call Method call (1) 122
Non-Precedence A q.enq(3) B p.enq(4) B p.void B q.deq() A q:void B q:3 Some method calls overlap one another Method call Method call (1) 123
Notation Given History H method executions m 0 and m 1 in H We say m 0 H m 1, if m 0 precedes m 1 m Relation m 0 H m 1 is a 0 m 1 Partial order Total order if H is sequential 124
Linearizability History H is linearizable if it can be extended to G by Appending zero or more responses to pending invocations Discarding other pending invocations So that G is equivalent to Legal sequential history S where G S 125
What is G S G = {a c,b c} S = {a b,a c,b c} a b G c time S (8) 126
Remarks Some pending invocations Took effect, so keep them Discard the rest Condition G S Means that S respects real-time order of G 127
Example A q.enq(3) B q.enq(4) B q:void B q.deq() B q:4 B q:enq(6) A. q.enq(3) B.q.enq(4) B.q.deq(4) time B. q.enq(6) 128
Example A q.enq(3) B q.enq(4) B q:void B q.deq() B q:4 B q:enq(6) Complete this pending invocation A. q.enq(3) B.q.enq(4) B.q.deq(3) B. q.enq(6) time 129
Example A q.enq(3) B q.enq(4) B q:void B q.deq() B q:4 B q:enq(6) A q:void Complete this pending invocation B.q.enq(3) B.q.enq(4) B.q.deq(4) B. q.enq(6) time 130
Example discard this one A q.enq(3) B q.enq(4) B q:void B q.deq() B q:4 B q:enq(6) A q:void B.q.enq(3) B.q.enq(4) B.q.deq(4) B. q.enq(6) time 131
Example discard this one A q.enq(3) B q.enq(4) B q:void B q.deq() B q:4 A q:void B.q.enq(3) B.q.enq(4) B.q.deq(4) time 132
Example A q.enq(3) B q.enq(4) B q:void B q.deq() B q:4 A q:void B.q.enq(3) B.q.enq(4) B.q.deq(4) time 133
Example A q.enq(3) B q.enq(4) B q:void B q.deq() B q:4 A q:void B q.enq(4) B q:void A q.enq(3) A q:void B q.deq() B q:4 B.q.enq(3) B.q.enq(4) B.q.deq(4) time 134
Example Equivalent sequential history A q.enq(3) B q.enq(4) B q:void B q.deq() B q:4 A q:void B q.enq(4) B q:void A q.enq(3) A q:void B q.deq() B q:4 B.q.enq(3) B.q.enq(4) B.q.deq(4) time 135
Concurrency How much concurrency does linearizability allow? When must a method invocation block? 136
Concurrency Focus on total methods Defined in every state Example: deq() that throws Empty exception Versus deq() that waits Why? Otherwise, blocking unrelated to synchronization 137
Concurrency Question: When does linearizability require a method invocation to block? Answer: never. Linearizability is non-blocking 138
Non-Blocking Theorem If method invocation A q.inv( ) is pending in history H, then there exists a response A q:res( ) such that H + A q:res( ) is linearizable 139
Proof Pick linearization S of H If S already contains Invocation A q.inv( ) and response, Then we are done. Otherwise, pick a response such that S + A q.inv( ) + A q:res( ) Possible because object is total. 140
Composability Theorem History H is linearizable if and only if For every object x H x is linearizable 141
Why Does Composability Matter? Modularity Can prove linearizability of objects in isolation Can compose independently-implemented objects 142
Reasoning About Lineraizability: Locking head 0 1 public T deq() throws EmptyException capacity-1 { y z lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } } 2 tail 143
Reasoning About Lineraizability: Locking public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } } finally { lock.unlock(); } Linearization points are when locks are released 144
More Reasoning: Lock-free public class LockFreeQueue { int head = 0, tail = 0; items = (T[]) new Object[capacity]; head capacity-1 0 1 y z 2 tail public void enq(item x) { while (tail-head == capacity); // busy-wait items[tail % capacity] = x; tail++; } public Item deq() { while (tail == head); // busy-wait Item item = items[head % capacity]; head++; return item; }} 145
More Reasoning public class LockFreeQueue { Linearization order is order head and tail fields modified int head = 0, tail = 0; items = (T[]) new Object[capacity]; public void enq(item x) { while (tail-head == capacity); // busy-wait items[tail % capacity] = x; tail++; } public Item deq() { while (tail == head); // busy-wait Item item = items[head % capacity]; head++; return item; }} 146
Strategy Identify one atomic step where method happens Critical section Machine instruction Doesn t always work Might need to define several different steps for a given method 147
Linearizability: Summary Powerful specification tool for shared objects Allows us to capture the notion of objects being atomic There is a lot of ongoing research in verification community to build tools that can verify/debug concurrent implementations wrt linearizability 148
Alternative: Sequential Consistency History H is Sequentially Consistent if it can be extended to G by Appending zero or more responses to pending invocations Discarding other pending invocations So that G is equivalent to a Legal sequential history S Where G S Differs from linearizability
Alternative: Sequential Consistency No need to preserve real-time order Cannot re-order operations done by the same thread Can re-order non-overlapping operations done by different threads Often used to describe multiprocessor memory architectures
Example time (5)
Example q.enq(x) time (5)
Example q.enq(x) q.deq(y) time (5)
Example q.enq(x) q.deq(y) q.enq(y) time (5)
Example q.enq(x) q.deq(y) q.enq(y) time (5)
Example q.enq(x) q.deq(y) q.enq(y) time (5)
Example q.enq(x) q.deq(y) q.enq(y) time (5)
Theorem Sequential Consistency is not a local property (and thus we lose composability )
FIFO Queue Example p.enq(x) q.enq(x) p.deq(y) time
FIFO Queue Example p.enq(x) q.enq(x) p.deq(y) q.enq(y) p.enq(y) q.deq(x) time
FIFO Queue Example p.enq(x) q.enq(x) p.deq(y) q.enq(y) p.enq(y) q.deq(x) History H time
H p Sequentially Consistent p.enq(x) q.enq(x) p.deq(y) q.enq(y) p.enq(y) q.deq(x) time
H q Sequentially Consistent p.enq(x) q.enq(x) p.deq(y) q.enq(y) p.enq(y) q.deq(x) time
Ordering imposed by p p.enq(x) q.enq(x) p.deq(y) q.enq(y) p.enq(y) q.deq(x) time
Ordering imposed by q p.enq(x) q.enq(x) p.deq(y) q.enq(y) p.enq(y) q.deq(x) time
Ordering imposed by both p.enq(x) q.enq(x) p.deq(y) q.enq(y) p.enq(y) q.deq(x) time
Combining orders p.enq(x) q.enq(x) p.deq(y) q.enq(y) p.enq(y) q.deq(x) time
Fact Most hardware architectures don t support sequential consistency Because they think it s too strong Here s another story
The Flag Example x.write(1) y.read(0) y.write(1) x.read(0) time
The Flag Example x.write(1) y.read(0) y.write(1) x.read(0) Each thread s view is sequentially consistent It went first time
The Flag Example x.write(1) y.read(0) y.write(1) x.read(0) Entire history isn t sequentially consistent time Can t both go first
The Flag Example x.write(1) y.read(0) y.write(1) x.read(0) Is this behavior really so wrong? We can argue either way time
Opinion1: It s Wrong This pattern Write mine, read yours Heart of mutual exclusion Peterson Bakery, etc. It s non-negotiable!
Opinion2: But It Should be Allowed Many hardware architects think that sequential consistency is too strong Too expensive to implement in modern hardware OK if flag principle violated by default Honored by explicit request
Memory Hierarchy On modern multiprocessors, processors do not read and write directly to memory. Memory accesses are very slow compared to processor speeds, Instead, each processor reads and writes directly to a cache
Memory Operations To read a memory location, load data into cache. To write a memory location update cached copy, Lazily write cached data back to memory
While Writing to Memory A processor can execute hundreds, or even thousands of instructions Why delay on every memory write? Instead, write back in parallel with rest of the program.
Bottomline.. Flag violation history is actually OK processors delay writing to memory Until after reads have been issued. Otherwise unacceptable delay between read and write instructions. Who knew you wanted to synchronize?
Who knew you wanted to synchronize? Writing to memory = mailing a letter Vast majority of reads & writes Not for synchronization No need to idle waiting for post office If you want to synchronize Announce it explicitly Pay for it only when you need it
Explicit Synchronization Memory barrier instruction Flush unwritten caches Bring caches up to date Compilers often do this for you Entering and leaving critical sections Expensive
Volatile In Java, can ask compiler to keep a variable up-to-date with volatile keyword Also inhibits reordering, removing from loops, & other optimizations
Real-World Hardware Memory Weaker than sequential consistency Examples: TSO, RMO, Intel x86 But you can get sequential consistency at a price OK for expert, tricky stuff assembly language, device drivers, etc. Linearizability more appropriate for high-level software
Critical Sections Easy way to implement linearizability Take sequential object Make each method a critical section Problems Blocking No concurrency
Linearizability Linearizability Operation takes effect instantaneously between invocation and response Uses sequential specification, locality implies composablity Good for high level objects
Correctness: Linearizability Sequential Consistency Not composable Harder to work with Good way to think about hardware models We will use linearizability as in the remainder of this course unless stated otherwise
Progress We saw an implementation whose methods were lock-based (deadlockfree) We saw an implementation whose methods did not use locks (lock-free) How do they relate?
Maximal vs. Minimal Minimal progress: in some suffix of H, some pending active invocation has a matching response (some method call eventually completes ).
Maximal vs. Minimal Minimal progress: in some suffix of H, some pending active invocation has a matching response (some method call eventually completes ).
Maximal vs. Minimal Minimal progress: in some suffix of H, some pending active invocation has a matching response (some method call eventually completes ). Maximal progress: in every suffix of H, every pending active invocation has a matching response (every method call always completes).
Maximal vs. Minimal Minimal progress: in some suffix of H, some pending active invocation has a matching response (some method call eventually completes ). Maximal progress: in every suffix of H, every pending active invocation has a matching response (every method call always completes).
Progress Conditions Deadlock-free: some thread trying to acquire the lock eventually succeeds. Starvation-free: every thread trying to acquire the lock eventually succeeds. Lock-free: some thread calling a method eventually returns. Wait-free: every thread calling a method eventually returns.
Progress Conditions Non-Blocking Blocking Everyone makes progress Someone makes progress Wait-free Lock-free Starvation-free Deadlock-free
Summary We will look at linearizable blocking and non-blocking implementations of objects.