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Impossibilities for Disjoint-Access Parallel Transactional Memory :

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Impossibilities for Disjoint-Access Parallel Transactional Memory :

[Guerraoui & Kapalka, SPAA 08]

[Attiya, Hillel & Milani, SPAA 09]

Alessia Milani

Read X

Write X

Read Z

Read Y

- A transaction is a sequence of operations by a single process on a set of shared data items (data set) to be executed atomically
- Like in database systems

- A transaction ends either by committing
- all of its updates take effect
or by aborting

- no update is effective

- all of its updates take effect

ABORT

base obj

base obj

- Data representation for transactions and data items

-------------------------------------------------------

High-level

operations

on data items

Low-level primitives operations (read, write,

CAS…) on base objects (memory locations)

Algorithms

33

Serializability[Papadimitriou, 1979]

- Any interleaving of the transactions yields a result that can be achieved in a sequential execution of the same set of transactions (aserialization)
Strict Serializability[Papadimitriou, 1979]

- … and the serialization must preserve the real-time order of (non-overlapping) transactions

44

T1

X2

X1

T1

Read(Y)

Write(X1)

T3

T2

Write(X2)

T2

T3

Read(X2)

Read(X1)

T1

Disjoint data sets no contention

Data sets are connected may contend

T2

Improves scalability for large data structures by reducing interference

5

Inherent Limitations on TMs

Concurrently execute a low-level operation

[Israeli & Rappaport, 1994]

An STM implementation is disjoint access parallel if two transactions T1 and T2 contend on the same base object ONLY IFthe data sets of T1 and T2 are connected

The data sets of T1 and T2 either intersect or are connected via other transactions

66

6

Inherent Limitations on TMs

T1

X2

X1

T1

Read(Y)

Write(X1)

T3

T2

Write(X2)

T2

T3

Read(X2)

Read(X1)

[Guerraoui & Kapalka, SPAA 08]

- Two transactions conflict on a low level base object only if their data sets intersect
- T1 and T2 cannot contend on a same base object

T1

T2

Contend on the base object and one operation writes into it

- Allows read-read contention for not connected transactions
- But indirectly connected transactions cannot conflict

[Guerraoui & Kapalka, SPAA 08]

Theorem.No obstruction free TM isStrictly Disjoint Access Parallel

The proof is by contradiction

99

9

Before s : x and y both equal 0

After s : y =1

Read(w)0, Read(z)0

Write(x,1), Write(y,1)

s

T1

T1

Cmt

- Assume a strictly DAP obstruction free TM exists
- T1 runs solo commits (obstruction freedom)

Read(x)0,Write(w,1)

T2

Cmt

Before s : x and y both equal 0

After s : y =1

Read(w)0, Read(z)0

Write(x,1), Write(y,1)

s

T1

T1

- T2 runs solo commits (obstruction freedom)

Read(w)0, Read(z)0

Write(x,1), Write(y,1)

s

T1

T1

Read(x)0,Write(w,1)

T2

Cmt

Read(y)1,Write(z,1)

T3

Cmt

Before s : x and y both equal 0

After s : at least one between

x and y is equal 1

- T2 and T3 have disjoint data set T2 “invisible” to T3 (strictly DAP) T3 reads y equal 1
- T3 runs solo should commit (obstruction freedom)

Read(w)0, Read(z)0

Write(x,1), Write(y,1)

s

T1

T1

Read(x)0,Write(w,1)

T2

Cmt

- If T1 commits, the execution is not serializable because of the read by T2, but
- If T1 does not commit, the execution is not serializable because of the read by T3

Read(y)1,Write(z,1)

T3

Cmt

Contradiction to the existence of

a strict DAP obstruction free TM

- Previous theorem does not hold
- In fact…DAP can be ensured by an obstruction free TM implementation
- DSTM [Herlihy, Luchangco, Moir & Scherer]

1414

14

Transactions that only observe the data

- Empty write set

- Avoid contention for the memory

1515

15

Inherent Limitations on TMs

Transactions that only observe the data

- Empty write set

- Avoid contention for the memory

1616

16

Inherent Limitations on TMs

17

17

Theorem.There is no TM implementation that isDAPand hasinvisible and wait-free read-only transactions

The proof relies on the notion of flippable execution, originally presented to prove lower bounds for atomic snapshot objects

[Israeli & Shirazi] [Attiya, Ellen & Fatourou]

1818

18

Inherent Limitations on TMs

A complete transaction in which p1 writes l-1 to X1

A read-only transaction by q that reads X1 , X2

U0 … Ul-1 … Uk

Ek

p1

U1 … Ul …

p2

q

s1 … sl-1sl … sk

1919

U0 … Ul-1 … Uk

Ek

p1

U1 … Ul …

p2

q

s1 … sl-1sl … sk

Indistinguishable from executions where the order of (each pair of) consecutive updates is flipped…either forward or backward

2020

20

U0 … Ul-1 … Uk

U0 … Ul-1 … Uk

Ek

Fk

p1

p1

U1 … Ul …

U1 … Ul …

p2

p2

q

q

s1 … sl-1sl … sk

s1 … sl-1sl … sk

Backward flip

Lemma 1.In a flippable execution the read-only transaction cannot terminate successfully

- Relies on Strict Serializability

2222

22

Inherent Limitations on TMs

U0 … Ul-1 … Uk

Ek

p1

U1 … Ul …

p2

q

s1 … sl-1sl … sk

U0 Ul-1 Uk

U1 … Ul …

Serialization of Ek

Returns (l-1,l-2)

Serialization point

2323

23

Inherent Limitations on TMs

U0 … Ul-1 … Uk

Ek

p1

U1 … Ul …

p2

q

s1 … sl-1sl … sk

U0 Ul-1 Uk

U1 … Ul …

Serialization of Ek

U0 Ul -1 Uk

U1 … Ul …

Returns (l-1,l-2)

U0 … Ul-1 … Uk

Fk

p1

U1 … Ul …

p2

Still returns (l-1,l-2)

q

s1 … sl-1sl … sk

x

x

x

Backward flip

X1 = l-3

X2= l-2

X1 = l-3

X2= l

X1 = l-1

X2= l

Serialization of Fk

Lemma 2.In a DAP TM, two consecutive transactions writing to different data items do not contend on the same base object

2525

25

Last write to o

U1

p1

1

1

First access to o

U2

2

2

p2

By contradiction assume that U1 and U2 contend on a same base object

o is the last base object written by U1 that U2 accesses

2626

26

Last write to o

U1

p1

p1

1

1

First access to o

U2

2

2

p2

p2

U1

1

1

2

2

U2

Serial execution of U1 and U2

Overlapping execution of U1 and U2

- U1 and U2 have disjoint data sets & contend on a base object

Not a DAP Implementation

- The steps of the read-only transaction can be removed (since it is invisible)
- Since their data sets are disjoint, transactions Ul & Ul-1 do not “communicate” (by Lemma 2)
- Can be flipped

2828

28

Inherent Limitations on TMs

By Lemma 1, the read-only transaction cannot terminate successfully

If aborts, we can apply the same argument again…

2929

29

Inherent Limitations on TMs

In a strict serializable DAP TM, where read-only transactions are wait-free, a transaction with a data set of size t must write to t-1 base objects

OUR RESULTS

STILL HOLD

- If a transaction runs alone from a quiescent configuration then it terminates successfully
- Obstruction-freedom
- A transaction (eventually) running solo, terminates successfully

- Weakly progressiveness

OUR RESULTS

STILL HOLD

OPEN PROBLEM

- Serializability
- Snapshot Isolation
- Causal Consistency
- Causal Serializability

- Our impossibility result still holds when considering a weakernotion of DAP thatallows read-read contention (not connected transactions can read a same base object)
- T1 and T2 can read a same base object

Theorem.No obstruction free TM isStrictly DAP

Theorem.There is no TM implementation that isDAPand hasinvisible and wait-free read-only transactions

3434