Domain Extension of Lock-Freedom and Wait-Freedom for Group Computations

2026-07-12

AI Summary

Traditional definitions of lock-freedom and wait-freedom apply only to single-threaded tasks and are inadequate for characterizing group computing scenarios involving multi-threaded collaboration. This work formally extends these liveness properties to the domain of group computation, introducing group lock-freedom (gl-freedom) and group wait-freedom (gw-freedom). The proposed definitions strictly degenerate to their classical counterparts in the single-threaded case and are rigorously validated through consistency checks and boundary analyses grounded in concurrent computation theory. By distinguishing program behaviors under diverse collaboration patterns, this framework avoids the oversimplification of categorizing heterogeneous concurrent programs merely as deadlock-free or livelock-free, thereby significantly enhancing the precision of concurrency system classification and analysis.

Abstract

A domain extension of a definition refers to broadening the scope of a definition so that it applies to a larger set of cases than originally specified. The notion of lock-free and wait-free computation is designed for the domain of tasks that are completed by a single thread (in competition with other threads). The goal of this paper is to extend the definition of lock-freedom and wait-freedom to group-computations (denoted by gl-freedom and gw-freedom) that require that the task at hand must be completed by a collaboration between multiple threads. When extending a definition, certain constraints must be respected: the new domain must remain logically consistent with the original meaning, the extension should not introduce contradictions or ambiguities, and it must preserve the essential properties that make the definition valid and useful. We demonstrate this by showing that our extended definition is consistent with the original definition when the group consists of a single thread. We note that extension allows us to characterize programs in a new domain (distributed computing, NUMA computation systems, systems with private data for different threads, etc.) instead of relegating them to be in the same category (deadlock/livelock-free) without regard to the actual properties of that program. We also illustrate this definition with various examples.

Problem

• lock-freedom
• wait-freedom
• group computations
• domain extension
• concurrent programming

Innovation

• lock-freedom
• wait-freedom
• group computations
• domain extension
• concurrent correctness