Quantifiability: Correctness of Concurrent Programs in Vector Space
Victor Cook, Christina Peterson, Zachary Painter, Damian Dechev · 2021
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. Analysis is facilitated with linear algebra, better supported and of much more efficient time complexity than traditional combinatorial methods.