Inherent limitations on DAP TMs 1 Inherent Limitations on Disjoint-Access Parallel Transactional Memory Hagit Attiya, Eshcar Hillel, Alessia Milani Technion

Inherent limitations on DAP TMs 2 Complexity Bounds for STMs: Why? Indicate futile design choices Elucidate expectations (specification) Spell out assumptions (models of the architecture)

Inherent limitations on DAP TMs 3 33 DAP: Disjoint Access Parallelism T1T1 Read(Y) Write(X 1 ) T2T2 Write(X 2 ) T3T3 Read(X 2 ) Read(X 1 ) Disjoint data sets  no contention Data sets are connected  may contend Y X2X2 X1X1 T3T3 T1T1 Improves scalability for large data structures by reducing interference

Inherent limitations on DAP TMs 4 44 Optimizing for Read-Only Transactions Transactions that do not modify the data should Be invisible (not write to low-level objects)  Avoid contention for the memory Always terminate successfully (wait-free)

Inherent limitations on DAP TMs 5 55 Some Known STMs… Read-only Tx termination Invisible read-only Tx DAPAlgorithm  [Herlihy, Luchangco, Moir & Scherer]  [Avni & Shavit]  [Riegel, Felber & Fetzer] Coincidence or inherent tradeoff ?

Inherent limitations on DAP TMs 6 66 Inherent Tradeoff Theorem. There is no TM implementation that is DAP and has invisible & wait-free read-only transactions The paper also shows a lower bound: Theorem. A transaction with a data set of size t must write to t-1 base objects Both proofs utilize the flippable execution, used to prove lower bounds for atomic snapshot objects [Israeli & Shirazi] [Attiya, Ellen & Fatourou]

Inherent limitations on DAP TMs 7 Flippable Execution w/ 2 Updaters p1p1 p2p2 q s 1 … s l-1 s l … s k U 1 … U l … U 0 … U l-1 … U k A complete transaction in which p 1 writes l-1 to X 1 A read-only transaction by q that reads X 1, X 2 EkEk

Inherent limitations on DAP TMs 8 Flippable Execution w/ 2 Updaters p1p1 p2p2 q s 1 … s l-1 s l … s k U 1 … U l … U 0 … U l-1 … U k EkEk Indistinguishable from executions where the order of (each pair of) updates is flipped… In one of two ways (forward and backward).

Inherent limitations on DAP TMs 9 Flippable Execution: Backward Flip p1p1 p2p2 q s 1 … s l-1 s l … s k U 1 … U l … U 0 … U l-1 … U k EkEk p1p1 p2p2 q s 1 … s l-1 s l … s k U 1 … U l … U 0 … U l-1 … U k Backward Flip

Inherent limitations on DAP TMs 10 Lemma 1. The read-only transaction of q cannot terminate successfully Relies on strict serializabitly (~linearizability) The serialization of committed transactions must preserve the real-time order of non- overlapping transactions Why Flippable Executions?

Inherent limitations on DAP TMs 11 Serialization of E k p1p1 p2p2 q s 1 … s l-1 s l … s k U 1 … U l … U 0 … U l-1 … U k EkEk U 1 … U l …U 0 U l-1 U k Serialization of E k : Serialization point Returns (l-1,l-2)

Inherent limitations on DAP TMs 12 Nowhere to Serialize p1p1 p2p2 q s 1 … s l-1 s l … s k U 1 … U l … U 0 … U l-1 … U k EkEk U 1 … U l …U 0 U l-1 U k Serialization Returns (l-1,l-2) p1p1 p2p2 q s 1 … s l-1 s l … s k U 1 … U l … U 0 … U l-1 … U k BW Flip Still returns (l-1,l-2) U 1 … U l U l-1 … U k U0U0 Serialization Indistinguishable from some flip (say, backward)

Inherent limitations on DAP TMs 13 Completing the Proof Show that a flippable execution exists  The read-only transaction is invisible  its steps can be removed  Transactions U l & U l-1 have disjoint data sets  U l & U l-1 do not “communicate” (by DAP)  U l & U l-1 can be flipped  By Lemma 1, the read-only transaction cannot terminate successfully  If aborts, can apply the same argument again…

Inherent limitations on DAP TMs 14 Complexity Bounds for STMs: What are the implications? Adapt your expectations  What STM guarantees (e.g. consistency)  What you measure: Best case, average case Special workloads

Inherent limitations on DAP TMs 15 Weaker Liveness Condition If a transaction runs alone from a quiescent configuration then it terminates successfully Weakly progressive blocking implementation [Guerraoui & Kapalka] OUR RESULTS STILL HOLD

Inherent limitations on DAP TMs 16 Serializability Snapshot Isolation Virtual world consistency Causal consistency Causal serializability 16 Weaker Consistency Conditions OUR RESULTS STILL HOLD OPEN PROBLEM

Inherent limitations on DAP TMs 17 Thank you! [paper in SPAA 09]

Inherent limitations on DAP TMs 18 Also a Lower Bound A transaction with a data set of size t must write to t-1 base objects  Relies on a stronger notion of DAP that does not allow even concurrent reads [Israeli & Rappaport]