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.

We verify the correctness of a variety of mutual exclusion algorithms through model checking. We look at algorithms where communication is via shared read/write registers, where those registers can be atomic or non-atomic. For the verification of liveness properties, it is necessary to assume a completeness criterion to eliminate spurious counterexamples. We use justness as completeness criterion. Justness depends on a concurrency relation; we consider several such relations, modelling different assumptions on the working of the shared registers. We present executions demonstrating the violation of correctness properties by several algorithms, and in some cases suggest improvements.

When verifying liveness properties on a transition system, it is often necessary to discard spurious violating paths by making assumptions on which paths represent realistic executions. Capturing that some property holds under such an assumption in a logical formula is challenging and error-prone, particularly in the modal $μ$-calculus. In this paper, we present template formulae in the modal $μ$-calculus that can be instantiated to a broad range of liveness properties. We consider the following assumptions: progress, justness, weak fairness, strong fairness, and hyperfairness, each with respect to actions. The correctness of these formulae has been proven.

We present process-algebraic models of multi-writer multi-reader safe, regular and atomic registers. We establish the relationship between our models and alternative versions presented in the literature. We use our models to formally analyse by model checking to what extent several well-known mutual exclusion algorithms are robust for relaxed atomicity requirements. Our analyses refute correctness claims made about some of these algorithms in the literature.