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.

We address this question, considering two type systems not covered in prior work: Kokke etal’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 relate the classes of deadlock-free processes induced by HCP and P. We prove that our results hold under both synchronous and asynchronous communication.

Our results provide new insights into the essential mechanisms involved in statically avoiding deadlocks in concurrency.