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Automatic generation of precise and useful commutativity conditions. (English) Zbl 1423.68115
Beyer, Dirk (ed.) et al., Tools and algorithms for the construction and analysis of systems. 24th international conference, TACAS 2018, held as part of the European joint conferences on theory and practice of software, ETAPS 2018, Thessaloniki, Greece, April 14–20, 2018. Proceedings. Part I. Cham: Springer. Lect. Notes Comput. Sci. 10805, 115-132 (2018).
Summary: Reasoning about commutativity between data-structure operations is an important problem with applications including parallelizing compilers, optimistic parallelization and, more recently, Ethereum smart contracts. There have been research results on automatic generation of commutativity conditions, yet we are unaware of any fully automated technique to generate conditions that are both sound and effective.
We have designed such a technique, driven by an algorithm that iteratively refines a conservative approximation of the commutativity (and non-commutativity) condition for a pair of methods into an increasingly precise version. The algorithm terminates if/when the entire state space has been considered, and can be aborted at any time to obtain a partial yet sound commutativity condition. We have generalized our work to left-/right-movers [R. J. Lipton, Commun. ACM 18, 717–721 (1975; Zbl 0316.68015)] and proved relative completeness. We describe aspects of our technique that lead to useful commutativity conditions, including how predicates are selected during refinement and heuristics that impact the output shape of the condition.
We have implemented our technique in a prototype open-source tool Servois. Our algorithm produces quantifier-free queries that are dispatched to a back-end SMT solver. We evaluate Servois through two case studies: (i) We synthesize commutativity conditions for a range of data structures including Set, HashTable, Accumulator, Counter, and Stack. (ii) We consider an Ethereum smart contract called BlockKing, and show that Servois can detect serious concurrency-related vulnerabilities and guide developers to construct robust and efficient implementations.
For the entire collection see [Zbl 1408.68006].

68P05 Data structures
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
CVC4; Servois; Solidity
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