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

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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

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Coarse-grained locking Top Inefficient as only one thread operates on the list at a time NULL

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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...

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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 , Calcagno , Amit , Manevich , Vafeiadis 2009] Termination ?

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Non-blocking concurrency: Treiber's stack Top NULL 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; } struct Node { Node *next; data_t val; } *Top;

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Treiber's non-blocking stack: termination 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; } struct Node { Node *next; data_t val; } *Top; 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

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From lock-freedom to termination

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Lock-freedom of Treiber's stack Push or Id Shared state Rely/guarantee + separation logic for safety [Vafeiadis-Parkinson 2007] 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; } struct Node { Node *next; data_t val; } *Top; Pop or Id

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Lock-freedom of Treiber's stack Push or Id 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; } struct Node { Node *next; data_t val; } *Top; Pop or Id

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Lock-freedom of Treiber's stack The do loops terminate if no-one else executes Push or Pop infinitely often No-one executes Push or Pop infinitely often Hence, push and pop terminate Push or Id 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; } 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)); } struct Node { Node *next; data_t val; } *Top; Pop or Id

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Layered proof “I execute only Push, Pop, or Id” “I don’t execute Push or Pop infinitely often” “I terminate” “I execute only Push, Pop, or Id”

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Layered proof Formalised in a logic for liveness and heaps Guarantees of the form

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Run the safety checker: Iteratively eliminate actions: Proof search strategy Proof valid for an arbitrary number of threads

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Case studies Treiber's stack [Treiber 1986] HSY stack [Hendler ] Non-blocking queue [Michael, Scott 1996] Linked list [Michael 2002] RDCSS [Harris ]

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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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