Linearizability of concurrent data structures is usually proved by monolithic simulation arguments relying on the identification of the so-called linearization points. Regrettably, such proofs, whether manual or automatic, are often complicated and scale poorly to advanced non-blocking concurrency patterns, such as helping and optimistic updates. In response, we propose a more modular way of checking linearizability of concurrent queue algorithms that does not involve identifying linearization points. We reduce the task of proving linearizability with respect to the queue specification to establishing four basic properties, each of which can be proved independently by simpler arguments. As a demonstration of our approach, we verify the Herlihy and Wing queue, an algorithm that is challenging to verify by a simulation proof.
Linearizability was first introduced by Herlihy and Wing @cite_8 , who also presented the HW queue as an example whose linearizability cannot be proved by a simple forward simulation where each method performs its effects instantaneously at some point during its execution. The problem is, as we have seen, that neither of @math or @math can be given as the (unique) linearization point of @math events, because the way in which two concurrent enqueues are ordered may depend on not-yet-completed concurrent @math events. In other words, one cannot simply define a mapping from the concrete HW queue states to the queue specification states. Nevertheless, Herlihy and Wing do not dismiss the linearization point technique completely, as we do, but instead construct a proof where they map concrete states to non-empty sets of specification states.
@cite_8
27871822 1503130891 2109717427 1543180701
Linearisability is the standard correctness criterion for concurrent data structures. In this paper, we present a sound and complete proof technique for linearisability based on backward simulations. We exemplify this technique by a linearisability proof of the queue algorithm presented in Herlihy and Wing's landmark paper. Except for the manual proof by them, none of the many other current approaches to checking linearisability has successfully treated this intricate example. Our approach is grounded on complete mechanisation: the proof obligations for the queue are verified using the interactive prover KIV, and so is the general soundness and completeness result for our proof technique. An execution containing operations performing queries or updating a concurrent object is linearizable w.r.t an abstract implementation (called specification) iff for each operation, one can associate a point in time, called linearization point, such that the execution of the operations in the order of their linearization points can be reproduced by the specification. Finding linearization points is particularly difficult when they do not belong to the operations's actions. This paper addresses this challenge by introducing a new technique for rewriting the implementation of the concurrent object and its specification such that the new implementation preserves all executions of the original one, and its linearizability (w.r.t. the new specification) implies the linearizability of the original implementation (w.r.t. the original specification). The rewriting introduces additional combined methods to obtain a library with a simpler linearizability proof, i.e., a library whose operations contain their linearization points. We have implemented this technique in a prototype, which has been successfully applied to examples beyond the reach of current techniques, e.g., Stack Elimination and Fetch&Add. Linearizability is one of the main correctness criteria for implementations of concurrent data structures. A data structure is linearizable if its operations appear to execute atomically. Verifying linearizability of concurrent unbounded linked data structures is a challenging problem because it requires correlating executions that manipulate (unbounded-size) memory states. We present a static analysis for verifying linearizability of concurrent unbounded linked data structures. The novel aspect of our approach is the ability to prove that two (unboundedsize) memory layouts of two programs are isomorphic in the presence of abstraction. A prototype implementation of the analysis verified the linearizability of several published concurrent data structures implemented by singly-linked lists. Linearizability, the key correctness condition that most optimized concurrent object implementations comply with, imposes tight synchronization between the object concurrent operations. This tight synchronization usually comes with a performance and scalability price. Yet, these implementations are often employed in an environment where a more relaxed linearizability condition suffices, where strict linearizability is not a must. Here we provide a quantitative definition of limited non-determinism, a notion we call Quasi Linearizability. Roughly speaking an implementation of an object is quasi linearizable if each run of the implementation is at a bounded "distance" away from some linear run of the object. However, as we show the limited distance has to be relative to some operations but not all. Following the definition we provide examples of quasi concurrent implementations that out perform state of the art standard implementations due to the relaxed requirement. Finally we show that the Bitonic Counting Network non-deterministic behavior can be quantified using our Quasi Linearizable notion.