Verifying Concurrent Stacks by Divergence-Sensitive Bisimulation

The verification of linearizability -- a key correctness criterion for concurrent objects -- is based on trace refinement whose checking is PSPACE-complete. This paper suggests to use \emph{branching} bisimulation instead. Our approach is based on comparing an abstract specification in which object methods are executed atomically to a real object program. Exploiting divergence sensitivity, this also applies to progress properties such as lock-freedom. These results enable the use of \emph{polynomial-time} divergence-sensitive branching bisimulation checking techniques for verifying linearizability and progress. We conducted the experiment on concurrent lock-free stacks to validate the efficiency and effectiveness of our methods

Linearizability with Ownership Transfer

Linearizability is a commonly accepted notion of correctness for libraries of concurrent algorithms. Unfortunately, it assumes a complete isolation between a library and its client, with interactions limited to passing values of a given data type. This is inappropriate for common programming languages, where libraries and their clients can communicate via the heap, transferring the ownership of data structures, and can even run in a shared address space without any memory protection. In this paper, we present the first definition of linearizability that lifts this limitation and establish an Abstraction Theorem: while proving a property of a client of a concurrent library, we can soundly replace the library by its abstract implementation related to the original one by our generalisation of linearizability. This allows abstracting from the details of the library implementation while reasoning about the client. We also prove that linearizability with ownership transfer can be derived from the classical one if the library does not access some of data structures transferred to it by the client

Concurrent Data Structures Linked in Time

Arguments about correctness of a concurrent data structure are typically carried out by using the notion of linearizability and specifying the linearization points of the data structure's procedures. Such arguments are often cumbersome as the linearization points' position in time can be dynamic (depend on the interference, run-time values and events from the past, or even future), non-local (appear in procedures other than the one considered), and whose position in the execution trace may only be determined after the considered procedure has already terminated. In this paper we propose a new method, based on a separation-style logic, for reasoning about concurrent objects with such linearization points. We embrace the dynamic nature of linearization points, and encode it as part of the data structure's auxiliary state, so that it can be dynamically modified in place by auxiliary code, as needed when some appropriate run-time event occurs. We name the idea linking-in-time, because it reduces temporal reasoning to spatial reasoning. For example, modifying a temporal position of a linearization point can be modeled similarly to a pointer update in separation logic. Furthermore, the auxiliary state provides a convenient way to concisely express the properties essential for reasoning about clients of such concurrent objects. We illustrate the method by verifying (mechanically in Coq) an intricate optimal snapshot algorithm due to Jayanti, as well as some clients

Putting Strong Linearizability in Context: Preserving Hyperproperties in Programs That Use Concurrent Objects

It has been observed that linearizability, the prevalent consistency condition for implementing concurrent objects, does not preserve some probability distributions. A stronger condition, called strong linearizability has been proposed, but its study has been somewhat ad-hoc. This paper investigates strong linearizability by casting it in the context of observational refinement of objects. We present a strengthening of observational refinement, which generalizes strong linearizability, obtaining several important implications. When a concrete concurrent object refines another, more abstract object - often sequential - the correctness of a program employing the concrete object can be verified by considering its behaviors when using the more abstract object. This means that trace properties of a program using the concrete object can be proved by considering the program with the abstract object. This, however, does not hold for hyperproperties, including many security properties and probability distributions of events. We define strong observational refinement, a strengthening of refinement that preserves hyperproperties, and prove that it is equivalent to the existence of forward simulations. We show that strong observational refinement generalizes strong linearizability. This implies that strong linearizability is also equivalent to forward simulation, and shows that strongly linearizable implementations can be composed both horizontally (i.e., locality) and vertically (i.e., with instantiation). For situations where strongly linearizable implementations do not exist (or are less efficient), we argue that reasoning about hyperproperties of programs can be simplified by strong observational refinement of non-atomic abstract objects