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VERIFICATION OF A NON-BLOCKING
ARRAY-BASED QUEUE ALGORITHM
Nastaran Shafiei
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Outline
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Algorithm Description
Algorithm Implementation
Verification
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Simulating Shared Variables
Linearizability
Java Pathfider Results
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The Algorithm
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Finite array, Q
Counters, FRONT and REAR
Operations: enqueue, dequeue
Elements of the queue
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Using compare-and-swap
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Implementation
NonblockingQueue
Enqueue
L: int
Q: AtomicLongArray
REAR: AtomicLong
FRONT: AtomicLong
getValPart(long queue)
getRefPart(long var)
getQueueItem(int val, int ref)
main(String[] args)
Dequeue
val: int
Enqueue(int value)
void run()
void run()
Thread
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…
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Shared Variables
public static AtomicLongArray Queue;
public static AtomicLong REAR;
public static AtomicLong FRONT;
Atomic variables
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Extend the concept of volatile variables
compareAndSet()
not supported by java pathfinder
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Simulating Atomic Variables
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AtomicLongArray
long array
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AtomicLong
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Using volatile keyword
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Simulating compareAndSwap()
long
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synchronized method
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Atomic execution methods
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beginAtomic() and endAtomic()
Declared in gov.nasa.jpf.jvm.Verify
Atomic block with respect to the whole program
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Linearizability
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Correctness condition
Definition:
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every concurrent execution = some legal sequential execution
Linearization point (enqueue)
A
C
B
Enqueue process:
Queue.compareAndSet( i, expected, newItem) = true
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Linearizability
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Linearization point (dequeue)
A
C
B
Dequeue process:
Queue.compareAndSet( i, expected, emptyItem)=true
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To prove linearizability
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Invariants were developed describing expected properties of the
shared variables.
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Linearizability
Auxiliary variables
Shared Variables
long r
REAR
long f
FRONT
long aq[]
Q[]
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Linearizability
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At enqueue linearization point:
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aq[r%L] = newItem
r++
At dequeue linearization point:
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aq[f%L] = emptyItem
f++
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Linearizability
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Invariant
Place of assertion
REAR == r-1
Enqueue linearization point
FRONT == f-1
Dequeue linearization point
aq[r%L] == Q[REAR%L]
synchronized CAS of REAR
aq[f%L] == Q[FRONT%L]
synchronized CAS of FRONT
Assertion method
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Declared in gov.nasa.jpf.jvm.Verify
public static void assert ( boolean b)
Checks that b evaluates to true
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Java Pathfinder Results
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Using beginAtomic() and endAtomic()
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Purpose: Simulate CAS/cut down state space
Jpf killed a thread and exited (even for 1 thread)
Using synchronized method to simulate CAS
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Up to 3 threads: no errors detected
4 threads:
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DFS : no errors detected
BFS gave Out.MemoryError : GC overhead limit exceeded
More: Out.MemoryError
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Questions?
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