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Impossibilities for Disjoint-Access Parallel Transactional Memory :

This article discusses the limitations of implementing disjoint-access parallelism and optimizing for read-only transactions in parallel transactional memory systems.

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Impossibilities for Disjoint-Access Parallel Transactional Memory :

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  1. Impossibilities for Disjoint-Access Parallel Transactional Memory : [Guerraoui & Kapalka, SPAA 08] [Attiya, Hillel & Milani, SPAA 09] Alessia Milani

  2. Read X Write X Read Z Read Y Transactional Synchronization • 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 ABORT

  3. base obj base obj Implementing Transactional Memory in Software • 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

  4. TM must provide 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

  5. T1 X2 X1 T1 Read(Y) Write(X1) T3 T2 Write(X2) T2 T3 Read(X2) Read(X1) DAP : Disjoint Access Parallelism 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

  6. Concurrently execute a low-level operation DAP : More Formally [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

  7. T1 X2 X1 T1 Read(Y) Write(X1) T3 T2 Write(X2) T2 T3 Read(X2) Read(X1) Strict Disjoint Access Parallelism [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

  8. Strict DAP versus DAP • Allows read-read contention for not connected transactions • But indirectly connected transactions cannot conflict

  9. An impossibility [Guerraoui & Kapalka, SPAA 08] Theorem.No obstruction free TM isStrictly Disjoint Access Parallel The proof is by contradiction 99 9

  10. 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 By contradiction Cmt • Assume a strictly DAP obstruction free TM exists • T1 runs solo  commits (obstruction freedom)

  11. Read(x)0,Write(w,1) T2 Cmt Proof 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)

  12. 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 Proof 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)

  13. Completing the Proof 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

  14. …with Disjoint Access Parallel • Previous theorem does not hold • In fact…DAP can be ensured by an obstruction free TM implementation • DSTM [Herlihy, Luchangco, Moir & Scherer] 1414 14

  15. Optimizing for Read-Only Transactions Transactions that only observe the data • Empty write set • Be invisible (not write to base objects) • Avoid contention for the memory • Always terminate successfully (wait-free) 1515 15 Inherent Limitations on TMs

  16. Optimizing for Read-Only Transactions Transactions that only observe the data • Empty write set • Be invisible (not write to base objects) • Avoid contention for the memory • Always terminate successfully (wait-free) 1616 16 Inherent Limitations on TMs

  17. Some Known STMs… 17 17

  18. Inherent Tradeoff 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

  19. A complete transaction in which p1 writes l-1 to X1 A read-only transaction by q that reads X1 , X2 Flippable Execution w/ 2 Updaters U0 … Ul-1 … Uk Ek p1 U1 … Ul … p2 q s1 … sl-1sl … sk 1919

  20. U0 … Ul-1 … Uk Ek p1 U1 … Ul … p2 q s1 … sl-1sl … sk Flippable Execution w/ 2 Updaters Indistinguishable from executions where the order of (each pair of) consecutive updates is flipped…either forward or backward 2020 20

  21. 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 Flippable Execution: Backward Flip Backward flip

  22. Lemma 1.In a flippable execution the read-only transaction cannot terminate successfully • Relies on Strict Serializability 2222 22 Inherent Limitations on TMs

  23. U0 … Ul-1 … Uk Ek p1 U1 … Ul … p2 q s1 … sl-1sl … sk U0 Ul-1 Uk U1 … Ul … Serialization of Ek Serialization of Ek Returns (l-1,l-2) Serialization point 2323 23 Inherent Limitations on TMs

  24. 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 … Nowhere to Serialize 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

  25. Constructing a Flippable Execution Lemma 2.In a DAP TM, two consecutive transactions writing to different data items do not contend on the same base object 2525 25

  26. Last write to o U1 p1 1 1 First access to o U2 2 2 p2 Proof of Lemma 2 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

  27. Last write to o U1 p1 p1 1 1 First access to o U2 2 2 p2 p2 U1 1 1 2 2 U2 Proof of Lemma 2 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

  28. A flippable execution exists • 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

  29. Completing the Proof 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

  30. Also a lower bound 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

  31. OUR RESULTS STILL HOLD Weaker Liveness Condition • If a transaction runs alone from a quiescent configuration then it terminates successfully • Obstruction-freedom • A transaction (eventually) running solo, terminates successfully • Weakly progressiveness

  32. OUR RESULTS STILL HOLD OPEN PROBLEM Weaker TM Consistency • Serializability • Snapshot Isolation • Causal Consistency • Causal Serializability

  33. Weakening DAP • 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

  34. To summarize Theorem.No obstruction free TM isStrictly DAP Theorem.There is no TM implementation that isDAPand hasinvisible and wait-free read-only transactions 3434

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