Towards Races in Linear Logic

TL;DR

This paper introduces non-deterministic HCP, extending linear logic-based process calculi to include non-determinism and races while maintaining deadlock freedom and strong typing.

Contribution

It presents a novel extension of HCP with non-determinism using bounded linear logic, addressing a key shortcoming in existing logic-based process calculi.

Findings

Captures non-deterministic choice in process calculus

Preserves deadlock freedom in the extended calculus

Provides a strongly-typed framework for non-deterministic processes

Abstract

Process calculi based in logic, such as $\pi$DILL and CP, provide a foundation for deadlock-free concurrent programming, but exclude non-determinism and races. HCP is a reformulation of CP which addresses a fundamental shortcoming: the fundamental operator for parallel composition from the $\pi$-calculus does not correspond to any rule of linear logic, and therefore not to any term construct in CP. We introduce non-deterministic HCP, which extends HCP with a novel account of non-determinism. Our approach draws on bounded linear logic to provide a strongly-typed account of standard process calculus expressions of non-determinism. We show that our extension is expressive enough to capture many uses of non-determinism in untyped calculi, such as non-deterministic choice, while preserving HCP's meta-theoretic properties, including deadlock freedom.