Proving highly-concurrent traversals correct
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 id...
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| Published in: | Proceedings of ACM on programming languages Vol. 4; no. OOPSLA; pp. 1 - 29 |
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13.11.2020
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| ISSN: | 2475-1421, 2475-1421 |
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| ArticleNumber | 128 |
| Author | Feldman, Yotam M. Y. Morrison, Adam Nanevski, Aleksandar Rinetzky, Noam Khyzha, Artem Shoham, Sharon Enea, Constantin |
| Author_xml | – sequence: 1 givenname: Yotam M. Y. surname: Feldman fullname: Feldman, Yotam M. Y. email: yotam.feldman@gmail.com organization: Tel Aviv University, Israel – sequence: 2 givenname: Artem surname: Khyzha fullname: Khyzha, Artem email: artkhyzha@mail.tau.ac.il organization: Tel Aviv University, Israel – sequence: 3 givenname: Constantin surname: Enea fullname: Enea, Constantin email: cenea@irif.fr organization: University of Paris Diderot, France – sequence: 4 givenname: Adam surname: Morrison fullname: Morrison, Adam email: mad@cs.tau.ac.il organization: Tel Aviv University, Israel – sequence: 5 givenname: Aleksandar orcidid: 0000-0002-4851-1075 surname: Nanevski fullname: Nanevski, Aleksandar email: aleks.nanevski@imdea.org organization: IMDEA Software Institute, Spain – sequence: 6 givenname: Noam surname: Rinetzky fullname: Rinetzky, Noam email: maon@cs.tau.ac.il organization: Tel Aviv University, Israel – sequence: 7 givenname: Sharon surname: Shoham fullname: Shoham, Sharon email: sharon.shoham@gmail.com organization: Tel Aviv University, Israel |
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| Cites_doi | 10.1145/3371113 10.1145/2491956.2462189 10.1017/S0956796818000151 10.1145/2684464.2684472 10.1145/2150976.2150998 10.5555/645958.676105 10.1007/978-3-662-46669-8_14 10.1145/2555243.2555267 10.1145/2555243.2555256 10.1145/2694344.2694359 10.1007/978-3-642-37036-6_17 10.1145/2688500.2688501 10.1145/2429069.2429134 10.1145/78969.78972 10.1145/2611462.2611471 10.1007/978-3-540-93900-9_27 10.1007/978-3-319-63390-9_28 10.1145/1040305.1040327 10.1145/1190216.1190261 10.1145/3158125 10.5555/1760631.1760646 10.1007/978-3-642-40047-6_25 10.1145/2168836.2168855 10.1145/2983990.2983999 10.1145/2555243.2555269 10.1145/3385412.3386029 10.1007/978-3-662-48653-5_24 10.1007/978-3-540-28644-8_4 10.1145/3360587 10.1007/978-3-540-28644-8_2 10.1145/2500365.2500600 10.1145/360051.360224 10.1145/1693453.1693488 10.1145/1706299.1706305 10.1007/978-3-662-44202-9_9 10.1007/978-3-662-46669-8_29 10.1109/TPDS.2011.159 10.1145/42201.42204 10.1007/978-3-642-14295-6_40 10.1142/S0129626416500158 |
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| Issue | OOPSLA |
| Keywords | traversal concurrent data structures proof framework linearizability traversal correctness |
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(e_1_2_2_33_1) 1983 Amit Daphna (e_1_2_2_2_1) 2007; 4590 e_1_2_2_41_1 e_1_2_2_62_1 Vafeiadis Viktor (e_1_2_2_64_1) 2016 e_1_2_2_8_1 e_1_2_2_26_1 e_1_2_2_47_1 Abdulla Parosh Aziz (e_1_2_2_1_1) 2013 e_1_2_2_13_1 e_1_2_2_38_1 e_1_2_2_59_1 Zhu He (e_1_2_2_65_1) 2015 Bouajjani Ahmed (e_1_2_2_7_1) 2015 e_1_2_2_11_1 Triplett Josh (e_1_2_2_57_1) 2011 e_1_2_2_51_1 e_1_2_2_19_1 e_1_2_2_53_1 Tu Stephen (e_1_2_2_58_1) 2013 e_1_2_2_17_1 e_1_2_2_34_1 e_1_2_2_55_1 e_1_2_2_15_1 e_1_2_2_36_1 e_1_2_2_25_1 e_1_2_2_48_1 e_1_2_2_5_1 e_1_2_2_3_1 Crain Tyler (e_1_2_2_14_1) 2013 e_1_2_2_40_1 e_1_2_2_42_1 e_1_2_2_9_1 e_1_2_2_29_1 Ellen Faith (e_1_2_2_21_1) 2010 e_1_2_2_46_1 Feldman Yotam M. Y. (e_1_2_2_23_1) 2010 Henzinger Thomas A. (e_1_2_2_28_1) 2013 Herlihy Maurice (e_1_2_2_30_1) Heller Steve (e_1_2_2_27_1) 2005 e_1_2_2_37_1 e_1_2_2_12_1 e_1_2_2_39_1 e_1_2_2_10_1 Michael Maged M. (e_1_2_2_45_1) 2002 Dragoi Cezara (e_1_2_2_20_1) 2013 McKenney Paul E. (e_1_2_2_44_1) 1998 e_1_2_2_52_1 e_1_2_2_31_1 e_1_2_2_54_1 e_1_2_2_18_1 e_1_2_2_56_1 e_1_2_2_16_1 e_1_2_2_35_1 O'Hearn P. W. (e_1_2_2_49_1) 2010 Shane (e_1_2_2_32_1) 2012 e_1_2_2_50_1 Vafeiadis Viktor (e_1_2_2_61_1) 2009; 5403 |
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