Proving Correctness of Concurrent Objects by Validating Linearization Points

Abstract

Concurrent data structures or CDS such as concurrent stacks, queues, sets etc. have become very popular in the past few years partly due to the rise of multi-core systems. Such concurrent CDSs offer great performance benefits over their sequential counterparts. But one of the greatest challenges with CDSs has been developing correct structures and then proving correctness of these structures. We believe that techniques that help prove correctness of these CDSs can also guide in developing new CDSs.An intuitive & popular techniques to prove correctness of CDSs is using Linearization Points or LPs. A LP is an (atomic) event in the execution interval of each method such that the execution of the entire method seems to have taken place in the instant of that event. One of the main challenges with the LP based approach is to identify the correct LPs of a CDS. Identifying the correct LPs can be deceptively wrong in many cases. In fact in many cases, the LP identified or even worse the CDS itself could be wrong. To address these issues, several automatic tools for verifying linearizability have been developed. But we believe that these tools don't provide insight to a programmer to develop the correct concurrent programs or identify the LPs.Considering the complexity of developing a CDS and verifying its correctness, we address the most basic problem of this domain in this paper: given the set of LPs of a CDS, how to show its correctness? We assume that we are given a CDS and its LPs. We have developed a hand-crafted technique of proving correctness of the CDSs by validating its LPs. As observed earlier, identifying the correct LPs is very tricky and erroneous. But since our technique is hand-crafted, we believe that the process of proving correctness might provide insight to identify the correct LPs, if the currently chosen LP is incorrect. We also believe that this technique might also offer the programmer some insight to develop more efficient variants of the CDS.The proposed proof technique can be applied to prove the correctness of several commonly used CDSs developed in literature such as Lock-free Linked based Sets, Skiplists etc. Our technique will also show correctness of CDSs in which the LPs of method might lie outside the methods (may seem to take effect in code of other method) such as lazy-list based set. To show the efficacy of this technique, we show the correctness of lazy-list and hoh-locking-list based set.