Scenario-Based Proofs for Concurrent Objects

Concurrent objects form the foundation of many applications that exploit multicore architectures and their importance has lead to informal correctness arguments, as well as formal proof systems. Correctness arguments (as found in the distributed computing literature) give intuitive descriptions of a...

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Bibliographic Details
Published in:Proceedings of ACM on programming languages Vol. 8; no. OOPSLA1; pp. 1294 - 1323
Main Authors: Enea, Constantin, Koskinen, Eric
Format: Journal Article
Language:English
Published: New York, NY, USA ACM 29.04.2024
Subjects:
Computing methodologies
Concurrent algorithms
Formal software verification
Logic and verification
Program reasoning
Software and its engineering
Theory of computation
concurrent objects
commutativity quotient
verification
linearizability
ISSN:2475-1421, 2475-1421
Online Access:Get full text
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Summary:Concurrent objects form the foundation of many applications that exploit multicore architectures and their importance has lead to informal correctness arguments, as well as formal proof systems. Correctness arguments (as found in the distributed computing literature) give intuitive descriptions of a few canonical executions or “scenarios” often each with only a few threads, yet it remains unknown as to whether these intuitive arguments have a formal grounding and extend to arbitrary interleavings over unboundedly many threads. We present a novel proof technique for concurrent objects, based around identifying a small set of scenarios (representative, canonical interleavings), formalized as the commutativity quotient of a concurrent object. We next give an expression language for defining abstractions of the quotient in the form of regular or context-free languages that enable simple proofs of linearizability. These quotient expressions organize unbounded interleavings into a form more amenable to reasoning and make explicit the relationship between implementation-level contention/interference and ADT-level transitions. We evaluate our work on numerous non-trivial concurrent objects from the literature (including the Michael-Scott queue, Elimination stack, SLS reservation queue, RDCSS and Herlihy-Wing queue). We show that quotients capture the diverse features/complexities of these algorithms, can be used even when linearization points are not straight-forward, correspond to original authors’ correctness arguments, and provide some new scenario-based arguments. Finally, we show that discovery of some object’s quotients reduces to two-thread reasoning and give an implementation that can derive candidate quotients expressions from source code.
ISSN:2475-1421
2475-1421
DOI:10.1145/3649857