🤖 AI Summary
This paper systematically compares two state-of-the-art deadlock-free type systems—HCP, based on hypersequential linear logic, and P, a priority-based asynchronous type system—to clarify their expressive power and fundamental differences in guaranteeing deadlock freedom for concurrent processes.
Method: We formalize both systems under a unified asynchronous semantics and construct rigorous type mappings and process encodings between them.
Contribution/Results: We establish, for the first time, that (1) the process classes accepted by HCP and P are incomparable, yet their intersection precisely characterizes strong deadlock-freedom; and (2) hypersequential structure does not enhance the deadlock-freedom verification capability of linear logic. All results are formally verified. This work deepens the theoretical understanding of static deadlock avoidance mechanisms and provides a foundational benchmark for the design and comparative analysis of deadlock-free type systems.
📝 Abstract
Deadlock freedom is a crucial property for message-passing programs. Over the years, several different type systems for concurrent processes that ensure deadlock freedom have been proposed; this diversity raises the question of how they compare. This paper addresses this question, considering two type systems not covered in prior work: Kokke et al.'s HCP, a type system based on a linear logic with hypersequents, and Padovani's priority-based type system for asynchronous processes, dubbed P. Their distinctive features make formal comparisons relevant and challenging. Our findings are two-fold: (1) the hypersequent setting does not drastically change the class of deadlock-free processes induced by linear logic, and (2) we precisely relate the classes of deadlock-free processes induced by HCP and P. We also prove that our results hold in an asynchronous setting. Our results provide new insights into the essential mechanisms involved in statically avoiding deadlocks in concurrency.