Synthesizing Commutativity Conditions Kshitij Bansal Eric Koskinen - - PowerPoint PPT Presentation

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synthesizing commutativity conditions

Synthesizing Commutativity Conditions Kshitij Bansal Eric Koskinen - - PowerPoint PPT Presentation

Nov 09, 2023 1.36k likes •1.64k views

Synthesizing Commutativity Conditions Kshitij Bansal Eric Koskinen Omer Tripp New York University IBM Research, New York IBM Research, New York United States United States United States Thread Thread Thread Thread 1 2 3 4 Thread

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Synthesizing Commutativity Conditions

Eric Koskinen IBM Research, New York United States Omer Tripp IBM Research, New York United States Kshitij Bansal New York University United States

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Concurrent HashMap Concurrent Queue Concurrent List

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put get enq deq add rm

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Concurrent HashMap Concurrent Queue Concurrent List

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put get enq deq add rm

Shared Memory

rd wr

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Concurrent HashMap Concurrent Queue Concurrent List

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put get enq deq add rm

Shared Memory

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Thread 1 Thread 3 Thread 2 Thread 4

Linearizability Commutativity

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Concurrent HashMap Concurrent Queue Concurrent List

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put get enq deq add rm

Shared Memory

rd wr

Thread 1 Thread 3 Thread 2 Thread 4

Linearizability Commutativity

Building blocks for Exploiting Multi-core Performance  (boosting, open-nesting, Celements et al TOCS’15) Sensible programming models Static/dynamic race detection Separation of concerns in verification . . .

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Serializable. … Opaque.

The PUSH/PULL Model

Push

⟨ht.get(5),_⟩

Pull

⟨ht.map(3,x),_⟩ ⟨ht.map(3,x),_⟩ ⟨q.enq(‘a’),_⟩ ⟨q.enq(‘a’),_,gUC⟩ ⟨ht.map(3,x),_,gUC⟩ ⟨ht.map(7,2),_,gUC⟩

PLDI 2015

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Serializable. … Opaque.

The PUSH/PULL Model

Push

⟨ht.get(5),_⟩

Pull

⟨ht.map(3,x),_⟩ ⟨ht.map(3,x),_⟩ ⟨q.enq(‘a’),_⟩ ⟨q.enq(‘a’),_,gUC⟩ ⟨ht.map(3,x),_,gUC⟩ ⟨ht.map(7,2),_,gUC⟩

PLDI 2015

Linearizable Commute

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Linearizable Commute

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Linearizable Commute

Reduce to Reachability Bouajjani et al. ICALP’15

Many techniques based on program logics

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Commute

add(x) ⋈ remove(y)

?

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Commute

add(x) ⋈ remove(y)

?

Joint work with Kshitij Bansal (NYU) and Omer Tripp (IBM)

New Technique

✓ Synthesize sound commutativity conditions ✓ Developed an encoding that allows us to reduce

commutativity to a format amenable to SMT solvers

✓ Relative completeness ✓ Implemented and applied to key data-structures

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Commute

Set Abstract Data Type S Example.

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Commute

Goal. Discover a condition that implies

add(x) ⋈ remove(y)

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Commute

Candidate commutativity condition φ Goal. Discover a condition that implies

add(x) ⋈ remove(y)

Strategy. ⋈ valid ⎞

φ … ⇒

⎛ ｜ ⎝ ⎠ ｜

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Commute

Candidate commutativity condition φ Goal. Discover a condition that implies

add(x) ⋈ remove(y)

Strategy. ⋈ valid ⎞

φ … ⇒

⎛ ｜ ⎝ ⎠ ｜

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Commute

Candidate commutativity condition φ Goal. Discover a condition that implies

add(x) ⋈ remove(y)

Strategy. ⋈ valid ⎞

φ … ⇒

⎛ ｜ ⎝ ⎠ ｜

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Commute

Candidate commutativity condition φ Goal. Discover a condition that implies

add(x) ⋈ remove(y)

Strategy. ⋈ valid ⎞

φ … ⇒

⎛ ｜ ⎝ ⎠ ｜ A SMT-friend encoding that does not introduce quantifiers (aside from outermost ∀) Translate partial specification to equivalent total specification.

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Commute

false false false

⋈ valid ⎞

H0 … ⇒

⎛ ｜ ⎝ ⎠ ｜ Abstraction Refinement Algorithm

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Commute

false false false

⋈ valid ⎞

H1 … ⇒

⎛ ｜ ⎝ ⎠ ｜

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Commute

false false false

⋈ valid ⎞

H’1 … ⇒

⎛ ｜ ⎝ ⎠ ｜

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Commute

false false false

⋈ valid ⎞

… ⇒

⎛ ｜ ⎝ ⎠ ｜

H2

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Commute

false false false

⋈ valid ⎞

… ⇒

⎛ ｜ ⎝ ⎠ ｜

H2

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Commute

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Commute

Challenges

1. Avoid introducing quantifier alternation

Translate partial specification to equivalent total specification.

2. Populating atomic predicates

Automatically extracted from the atoms of the transition system

3. Dynamic choice of next predicate

Counterexamples and “poke” heuristics.

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Commute

Thank you!