Proving highly-concurrent traversals correct

Yotam M.Y. Feldman, Artem Khyzha, Constantin Enea, Adam Morrison, Aleksandar Nanevski, Noam Rinetzky, Sharon Shoham

Research output: Contribution to journalArticlepeer-review


Modern highly-concurrent search data structures, such as search trees, obtain multi-core scalability and performance by having operations traverse the data structure without any synchronization. As a result, however, these algorithms are notoriously difficult to prove linearizable, which requires identifying a point in time in which the traversal's result is correct. The problem is that traversing the data structure as it undergoes modifications leads to complex behaviors, necessitating intricate reasoning about all interleavings of reads by traversals and writes mutating the data structure. In this paper, we present a general proof technique for proving unsynchronized traversals correct in a significantly simpler manner, compared to typical concurrent reasoning and prior proof techniques. Our framework relies only on sequential properties of traversals and on a conceptually simple and widely-applicable condition about the ways an algorithm's writes mutate the data structure. Establishing that a target data structure satisfies our condition requires only simple concurrent reasoning, without considering interactions of writes and reads. This reasoning can be further simplified by using our framework. To demonstrate our technique, we apply it to prove several interesting and challenging concurrent binary search trees: the logical-ordering AVL tree, the Citrus tree, and the full contention-friendly tree. Both the logical-ordering tree and the full contention-friendly tree are beyond the reach of previous approaches targeted at simplifying linearizability proofs.

Original languageEnglish
Article number128
JournalProceedings of the ACM on Programming Languages
Issue numberOOPSLA
StatePublished - 13 Nov 2020


FundersFunder number
European Union's Horizon 2020 research and innovation program
United States - Israel Binational Science Foundation
Horizon 2020 Framework Programme759102, 724464, 678177
Blavatnik Family Foundation
United States-Israel Binational Science Foundation2016260
Israel Science Foundation1996/18, 1810/18, 2005/17
Tel Aviv University
Ministerio de Ciencia e InnovaciónPGC2018-102210-B-I00
PAZY Foundation


    • concurrent data structures
    • linearizability
    • proof framework
    • traversal
    • traversal correctness


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