Shape predicates allow unbounded verification of linearizability using canonical abstraction

Canonical abstraction is a static analysis technique that represents states as 3-valued logical structures, and is able to construct finite representations of systems with infinite statespaces for verification. The granularity of the abstraction can be altered by the definition of instrumentation predicates, which derive their meaning from other predicates. We introduce shape predicates for preserving certain structures of the state during abstraction. We show that shape predicates allow linearizability to be verified for concurrent data structures using canonical abstraction alone, and use the approach to verify a stack and two queue algorithms. This contrasts with previous efforts to verify linearizability with canonical abstraction, which have had to employ other techniques as well

Verifying linearizability on TSO architectures

Linearizability is the standard correctness criterion for fine-grained, non-atomic concurrent algorithms, and a variety of methods for verifying linearizability have been developed. However, most approaches assume a sequentially consistent memory model, which is not always realised in practice. In this paper we define linearizability on a weak memory model: the TSO (Total Store Order) memory model, which is implemented in the x86 multicore architecture. We also show how a simulation-based proof method can be adapted to verify linearizability for algorithms running on TSO architectures. We demonstrate our approach on a typical concurrent algorithm, spinlock, and prove it linearizable using our simulation-based approach. Previous approaches to proving linearizabilty on TSO architectures have required a modification to the algorithm's natural abstract specification. Our proof method is the first, to our knowledge, for proving correctness without the need for such modification

Quiescent consistency: Defining and verifying relaxed linearizability

Concurrent data structures like stacks, sets or queues need to be highly optimized to provide large degrees of parallelism with reduced contention. Linearizability, a key consistency condition for concurrent objects, sometimes limits the potential for optimization. Hence algorithm designers have started to build concurrent data structures that are not linearizable but only satisfy relaxed consistency requirements. In this paper, we study quiescent consistency as proposed by Shavit and Herlihy, which is one such relaxed condition. More precisely, we give the first formal definition of quiescent consistency, investigate its relationship with linearizability, and provide a proof technique for it based on (coupled) simulations. We demonstrate our proof technique by verifying quiescent consistency of a (non-linearizable) FIFO queue built using a diffraction tree. © 2014 Springer International Publishing Switzerland

Faster linearizability checking via PP-compositionality

Linearizability is a well-established consistency and correctness criterion for concurrent data types. An important feature of linearizability is Herlihy and Wing's locality principle, which says that a concurrent system is linearizable if and only if all of its constituent parts (so-called objects) are linearizable. This paper presents $P$-compositionality, which generalizes the idea behind the locality principle to operations on the same concurrent data type. We implement $P$-compositionality in a novel linearizability checker. Our experiments with over nine implementations of concurrent sets, including Intel's TBB library, show that our linearizability checker is one order of magnitude faster and/or more space efficient than the state-of-the-art algorithm.Comment: 15 pages, 2 figure

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

Admit your weakness: Verifying correctness on TSO architectures

“The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-319-15317-9_22 ”.Linearizability has become the standard correctness criterion for fine-grained non-atomic concurrent algorithms, however, most approaches assume a sequentially consistent memory model, which is not always realised in practice. In this paper we study the correctness of concurrent algorithms on a weak memory model: the TSO (Total Store Order) memory model, which is commonly implemented by multicore architectures. Here, linearizability is often too strict, and hence, we prove a weaker criterion, quiescent consistency instead. Like linearizability, quiescent consistency is compositional making it an ideal correctness criterion in a component-based context. We demonstrate how to model a typical concurrent algorithm, seqlock, and prove it quiescent consistent using a simulation-based approach. Previous approaches to proving correctness on TSO architectures have been based on linearizabilty which makes it necessary to modify the algorithm’s high-level requirements. Our approach is the first, to our knowledge, for proving correctness without the need for such a modification

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