Quantifiability: Concurrent Correctness from First Principles
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by
Victor Cook, Christina Peterson, Zachary Painter, Damian Dechev
2019
Abstract
Architectural imperatives due to the slowing of Moore's Law, the broad
acceptance of relaxed semantics and the O(n!) worst case verification
complexity of generating sequential histories motivate a new approach to
concurrent correctness. Desiderata for a new correctness condition are that it
be independent of sequential histories, composable over objects, flexible as to
timing, modular as to semantics and free of inherent locking or waiting. We
propose Quantifiability, a novel correctness condition based on intuitive first
principles. Quantifiability models a system in vector space to launch a new
mathematical analysis of concurrency. The vector space model is suitable for a
wide range of concurrent systems and their associated data structures. This
paper formally defines quantifiablity with its system model and demonstrates
useful properties such as compositionality. Analysis is facilitated with linear
algebra, better supported and of much more efficient time complexity than
traditional combinatorial methods. We present results showing that quantifiable
data structures are highly scalable due to the usage of relaxed semantics, an
explicit implementation trade-off that is permitted by quantifiability.
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