On the Notions of Bounded Bypass, and How to Make any Deadlock-Free MUTEX Protocol Satisfy One of Them

2026-06-17

AI Summary

This work addresses the long-standing lack of a rigorous formal definition for “bounded bypass” in mutual exclusion protocols, a property that some protocols can only satisfy in a weakened form. The paper provides the first precise characterization of bounded bypass and introduces two intermediate variants: “post-gate bounded bypass” and “intermittent bounded bypass.” It further demonstrates that the Bar-David transformation algorithm can elevate any deadlock-free mutual exclusion protocol to satisfy the corresponding bounded bypass property: achieving quadratic-bounded bypass under atomic registers, and intermittent bounded bypass under safe or regular registers. All theoretical results are formally verified using rigorous formal methods and model checking.

Abstract

In the literature on mutual exclusion, bounded bypass has been used for a long time as a strengthening of starvation-freedom, but, to the best of our knowledge, it still lacks a satisfying definition as a liveness property on its own. Moreover, we have encountered MUTEX protocols for which this notion needs to be slightly weakened in order to be met. To solve these issues, we first provide a formal definition of bounded bypass (that also corrects a previous definition from Raynal) and then introduce the notions of post-doorway and intermittent bounded bypass, two liveness properties that lie between starvation-freedom and bounded bypass. Essentially, intermittent bounded bypass weakens bounded bypass by ignoring the possible bypasses that may happen during the execution of a certain finite set of write operations to shared registers. Orthogonally, post-doorway bounded bypass ignores the bypasses that may happen during a finite initial phase of the lock protocol. Furthermore, we study an algorithm proposed by Yoah Bar-David in 1998 to enhance the liveness properties of any deadlock-free MUTEX protocol and prove that: (1) in the setting of atomic registers, this algorithm upgrades any deadlock-free mutual exclusion protocol to a bounded bypass one, with a bound that is quadratic in the number of processes; and (2) in the setting of safe and regular registers, the very same algorithm ensures the intermittent version of bounded bypass, still with a quadratic (but slightly different) bound. Finally, we provide logical formulae for the different notions of bounded bypass defined in this paper and use them to confirm all claims made here, by using model checking. This had a positive impact on the theoretical development of the work, since it allowed us to identify and correct small mistakes/ambiguities in definitions and proofs.

Problem

• bounded bypass
• mutual exclusion
• liveness property
• starvation-freedom
• deadlock-free

Innovation

• bounded bypass
• mutual exclusion
• liveness properties
• model checking
• deadlock-free protocols