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Quantifiability: a concurrent correctness condition modeled in vector space

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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, compositional, flexible as to timing, modular as to semantics and free of inherent locking or waiting. We propose Quantifiability, a novel correctness condition that 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 quantifiability and demonstrates that quantifiability is compositional and non-blocking and that it implies observational refinement. Analysis is facilitated with linear algebra, better supported and of much more efficient time complexity than traditional combinatorial methods.

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Funding

This work was funded by NSF grant 1740095.

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Correspondence to Christina Peterson.

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This work was funded by NSF grant 1740095.

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Cook, V., Peterson, C., Painter, Z. et al. Quantifiability: a concurrent correctness condition modeled in vector space. Computing 105, 955–978 (2023). https://doi.org/10.1007/s00607-022-01092-3

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