Joint work with byron cook matthew parkinson and viktor vafeiadis
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Proving that non-blocking algorithms don't block. Alexey Gotsman University of Cambridge. Joint work with Byron Cook, Matthew Parkinson, and Viktor Vafeiadis. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A A A A.

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Joint work with Byron Cook, Matthew Parkinson, and Viktor Vafeiadis

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Proving that non-blocking algorithms don't block

Alexey Gotsman

University of Cambridge

Joint work with Byron Cook, Matthew Parkinson,

and Viktor Vafeiadis

TexPoint fonts used in EMF.

Read the TexPoint manual before you delete this box.: AAAAAAAAAAAA


Proving that non-blocking algorithms don't block

  • Automatically proving liveness properties of non-blocking concurrent algorithms

  • Stay awake: nice links between programming, logic, and automatic verification

    • Pick a class of programs

    • Pick an appropriate logic

    • Observe that proofs are simple and follow the same pattern

    • Infer proofs automatically

  • Best of both worlds: automatic tool + understanding of the algorithms


Coarse-grained locking

42

13

1

4

Top

NULL

Inefficient as only one

thread operates on the

list at a time


Non-blocking concurrency

  • Multiple threads operating on the data structure at the same time

  • Typical programming idiom:

    ...

    L:read from a part of the data structure

    do some work on the results

    try to change the data structure

    if interference is detected go to L

    ...


Non-blocking concurrency

  • Stacks, queues, skip lists, hash tables, etc.

  • Used in practice: e.g., java.util.concurrent

  • Complicated and hard to get right

  • Formal verification:

    • Safety properties

    • [Yahav+ 2003, Calcagno+ 2007, Amit+ 2007, Manevich+ 2008, Vafeiadis 2009]

    • Termination

?


Non-blocking concurrency: Treiber's stack

42

13

1

4

6

42

13

12

structNode {

Node *next;

data_t val;

} *Top;

void push(data_t v) {

Node *t, *x;

x = new Node();

x->val = v;

do {

t = Top;

x->next = t;

} while(!CAS(&Top,t,x));

}

data_t pop() {

Node *t, *x;

do {

t = Top;

if (t == NULL)

return EMPTY;

x = t->next;

} while(!CAS(&Top,t,x));

return t->val;

}

Top

NULL


Treiber's non-blocking stack: termination

structNode {

Node *next;

data_t val;

} *Top;

void push(data_t v) {

Node *t, *x;

x = new Node();

x->val = v;

do {

t = Top;

x->next = t;

} while(!CAS(&Top,t,x));

}

data_t pop() {

Node *t, *x;

do {

t = Top;

if (t == NULL)

return EMPTY;

x = t->next;

} while(!CAS(&Top,t,x));

return t->val;

}

  • push or pop may not terminate if other threads continually modify Top

  • However: some operation will always terminate

  • This talk: logic & tool for proving lock-freedom

lock-freedom


From lock-freedom to termination


Lock-freedom of Treiber's stack

data_t pop() {

Node *t, *x;

do {

t = Top;

if (t == NULL)

return EMPTY;

x = t->next;

} while(!CAS(&Top,t,x));

return t->val;

}

structNode {

Node *next;

data_t val;

} *Top;

void push(data_t v) {

Node *t, *x;

x = new Node();

x->val = v;

do {

t = Top;

x->next = t;

} while(!CAS(&Top,t,x));

}

Pushor Id

Pop or Id

Shared state

Rely/guarantee +

separation logic for safety

[Vafeiadis-Parkinson 2007]


Lock-freedom of Treiber's stack

data_t pop() {

Node *t, *x;

do {

t = Top;

if (t == NULL)

return EMPTY;

x = t->next;

} while(!CAS(&Top,t,x));

return t->val;

}

structNode {

Node *next;

data_t val;

} *Top;

void push(data_t v) {

Node *t, *x;

x = new Node();

x->val = v;

do {

t = Top;

x->next = t;

} while(!CAS(&Top,t,x));

}

Pushor Id

Pop or Id


Lock-freedom of Treiber's stack

data_t pop() {

Node *t, *x;

do {

t = Top;

if (t == NULL)

return EMPTY;

x = t->next;

} while(!CAS(&Top,t,x));

return t->val;

}

structNode {

Node *next;

data_t val;

} *Top;

void push(data_t v) {

Node *t, *x;

x = new Node();

x->val = v;

do {

t = Top;

x->next = t;

} while(!CAS(&Top,t,x));

}

Pushor Id

Pop or Id

  • The do loops terminate if no-one else executes Push or Pop infinitely often

  • No-one executes PushorPop infinitely often

  • Hence, push and popterminate


Layered proof

“I execute only Push, Pop, or Id”

“I execute only Push, Pop, or Id”

“I don’t execute Push or Pop infinitely often”

“I don’t execute Push or Pop infinitely often”

“I terminate”

“I terminate”


Layered proof

Formalised in a logic for liveness and heaps

Guarantees of the form


Proof search strategy

Proof valid for an arbitrary

number of threads

  • Run the safety checker:

  • Iteratively eliminate actions:


Case studies

  • Treiber's stack [Treiber 1986]

  • HSY stack [Hendler+ 2004]

  • Non-blocking queue [Michael, Scott 1996]

  • Linked list [Michael 2002]

  • RDCSS [Harris+ 2002]


Conclusion

  • Automatic method with proofs reflecting algorithm structure

  • Hope the general approach can be reused

  • Lock-based lock-free algorithms require more complex environment assumptions


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