Quantifiability: Concurrent Correctness from First Principles

TL;DR

Quantifiability introduces a new correctness condition for concurrent systems based on vector space modeling, enabling scalable, flexible, and modular analysis using linear algebra, addressing verification complexity and relaxing traditional constraints.

Contribution

It presents the first formal definition of quantifiability, a novel correctness condition that leverages vector space models and linear algebra for efficient concurrency analysis.

Findings

Quantifiability is compositional and independent of sequential histories.

Linear algebra facilitates more efficient analysis than traditional methods.

Quantifiability enables scalable and flexible concurrent data structures.

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 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 quantifiability 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 and propose entropy to evaluate the implementation trade-offs permitted by quantifiability.