Linearizability is the gold standard of correctness conditions for shared memory algorithms, and historically has been considered the practical equivalent of atomicity. However, it has been shown [1] that replacing atomic objects with linearizable implementations can affect the probability distribution of execution outcomes in randomized algorithms. Thus, linearizable objects are not always suitable replacements for atomic objects. A stricter correctness condition called strong linearizability has been developed and shown to be appropriate for randomized algorithms in a strong adaptive adversary model [1]. We devise several new lock-free strongly linearizable implementations from atomic registers. In particular, we give the first strongly linearizable lock-free snapshot implementation that uses bounded space. This improves on the unbounded space solution of Denysyuk and Woelfel [2]. As a building block, our algorithm uses a lock-free strongly linearizable ABA-detecting register. We obtain this object by modifying the wait-free linearizable ABA-detecting register of Aghazadeh and Woelfel [3], which, as we show, is not strongly linearizable. Aspnes and Herlihy [4] identified a wide class types that have wait-free linearizable implementations from atomic registers. These types require that any pair of operations either commute, or one overwrites the other. Aspnes and Herlihy gave a general wait-free linearizable implementation of such types, employing a wait-free linearizable snapshot object. Replacing that snapshot object with our lock-free strongly linearizable one, we prove that all types in this class have a lock-free strongly linearizable implementation from atomic registers.
Atomic shared objects, whose operations take place instantaneously, are a powerful abstraction for designing complex concurrent programs. Since they are not always available, they are typically substituted with software implementations. A prominent condition relating these implementations to their atomic specifications is linearizability, which preserves safety properties of the programs using them. However linearizability does not preserve hyper-properties, which include probabilistic guarantees of randomized programs: an adversary can greatly amplify the probability of a bad outcome. This un…
Linearizability is the gold standard among algorithm designers for deducing the correctness of a distributed algorithm using implemented shared objects from the correctness of the corresponding algorithm using atomic versions of the same objects. We show that linearizability does not suffice for this purpose when processes can exploit randomization, and we discuss the existence of alternative correctness conditions.
To implement a linearizable shared memory in synchronous message-passing systems it is necessary to wait for a time linear to the uncertainty in the latency of the network for both read and write operations. Waiting only for one of them suffices for sequential consistency. This paper extends this result to crash-prone asynchronous systems, proposing a distributed algorithm building a sequentially consistent shared snapshot memory on top of an asynchronous message-passing system where less than half of the processes may crash. We prove that waiting is needed only when a process invokes a read/s…
It has been proved that to implement a linearizable shared memory in synchronous message-passing systems it is necessary to wait for a time proportional to the uncertainty in the latency of the network for both read and write operations, while waiting during read or during write operations is sufficient for sequential consistency. This paper extends this result to crash-prone asynchronous systems. We propose a distributed algorithm that builds a sequentially consistent shared memory abstraction with snapshot on top of an asynchronous message-passing system where less than half of the processes…
A key way to construct complex distributed systems is through modular composition of linearizable concurrent objects. A prominent example is shared registers, which have crash-tolerant implementations on top of message-passing systems, allowing the advantages of shared memory to carry over to message-passing. Yet linearizable registers do not always behave properly when used inside randomized programs. A strengthening of linearizability, called strong linearizability, has been shown to preserve probabilistic behavior, as well as other hypersafety properties. In order to exploit composition and…
We prove that in asynchronous message-passing systems where at most one process may crash, there is no lock-free strongly linearizable implementation of a weak object that we call Test-or-Set (ToS). This object allows a single distinguished process to apply the set operation once, and a different distinguished process to apply the test operation also once. Since this weak object can be directly implemented by a single-writer single-reader (SWSR) register (and other common objects such as max-register, snapshot and counter), this result implies that there is no $1$-resilient lock-free strongly …
Impossibility Results for Strong Linearizability: The Difficulty of Consistent Refereeing
Technion - Israel Institute of Technology（以色列理工学院）；Universidad Nacional Autónoma de México (UNAM)（墨西哥国立自治大学）；LIX, Ecole Polytechnique, CNRS and Institut Polytechnique de Paris（巴黎综合理工学院LIX实验室、法国国家科学研究中心和巴黎理工学院）
In a seminal work, Golab et al. showed that a randomized algorithm that works with atomic objects may lose some of its properties if we replace the atomic objects that it uses with linearizable objects. It was not known whether the properties that can be lost include the important property of termination (with probability 1). In this paper, we first show that, for randomized algorithms, termination can indeed be lost. Golab et al. also introduced strong linearizability, and proved that strongly linearizable objects can be used as if they were atomic objects, even for randomized algorithms: the…
Linearizability, the traditional correctness condition for concurrent data structures is considered insufficient for the non-volatile shared memory model where processes recover following a crash. For this crash-recovery shared memory model, strict-linearizability is considered appropriate since, unlike linearizability, it ensures operations that crash take effect prior to the crash or not at all. This work formalizes and answers the question of whether an implementation of a data type derived for the crash-stop shared memory model is also strict-linearizable in the crash-recovery model. This …
The well known snapshot primitive in concurrent programming allows for n-asynchronous processes to write values to an array of single-writer registers and, for each process, to take a snapshot of these registers. In this paper we provide a formulation of the well known linearizability condition for snapshot algorithms in terms of the existence of certain mathematical functions. In addition, we identify a simplifying property of snapshot implementations we call "schedule-based algorithms". This property is natural to assume in the sense that as far as we know, every published snapshot algorithm…
Concurrent linearizable access to shared objects can be prohibitively expensive in a high contention workload. Many applications apply ad-hoc techniques to eliminate the need of synchronous atomic updates, which may result in non-linearizable implementations. We propose a new programming model which leverages such patterns for concurrent access to objects in a shared memory system. In this model, each thread maintains different views on the shared object - a thread-local view and a global view. As the thread-local view is not shared, it can be updated without incurring synchronization costs. T…
Big data processing systems often employ batched updates and data sketches to estimate certain properties of large data. For example, a CountMin sketch approximates the frequencies at which elements occur in a data stream, and a batched counter counts events in batches. This paper focuses on the correctness of concurrent implementations of such objects. Specifically, we consider quantitative objects, whose return values are from a totally ordered domain, with an emphasis on $(e,d)$-bounded objects that estimate a quantity with an error of at most $e$ with probability at least $1 - d$. The de f…
The implementation of registers from (potentially) weaker registers is a classical problem in the theory of distributed computing. Since Lamport's pioneering work [13], this problem has been extensively studied in the context of asynchronous processes with crash failures. In this paper, we investigate this problem in the context of Byzantine process failures, with and without process signatures. We first prove that, without signatures, there is no wait-free linearizable implementation of a 1-writer n-reader register from atomic 1-writer 1-reader registers. In fact, we show a stronger result, n…
We study the question of whether the "termination with probability 1" property of a randomized algorithm is preserved when one replaces the atomic registers that the algorithm uses with linearizable (implementations of) registers. We show that in general this is not so: roughly speaking, every randomized algorithm A has a corresponding algorithm A' that solves the same problem if the registers that it uses are atomic or strongly-linearizable, but does not terminate if these registers are replaced with "merely" linearizable ones. Together with a previous result shown in [15], this implies that …
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 set…
Multi-Version Concurrency Control (MVCC) is a common mechanism for achieving linearizable range queries in database systems and concurrent data-structures. The core idea is to keep previous versions of nodes to serve range queries, while still providing atomic reads and updates. Existing concurrent data-structure implementations, that support linearizable range queries, are either slow, use locks, or rely on blocking reclamation schemes. We present EEMARQ, the first scheme that uses MVCC with lock-free memory reclamation to obtain a fully lock-free data-structure supporting linearizable insert…
We show that for one-shot problems - problems where a processor executes a single operation-execution - timing constraints can be captured by conditions on the relation between original outputs and supplementary snapshots. In addition to the dictionary definition of the word snapshot, in distributed computing snapshots also stand for a task that imposes relation among sets which are output of processors. Hence, constrains relating the timing between operation-executions of processors can be captured by the sets relation representing a task. This allows to bring to bear techniques developed for…
In this work, we propose the $λ$-scanner snapshot, a variation of the snapshot object, which supports any fixed amount of $0 < λ\leq n$ different $SCAN$ operations being active at any given time. Whenever $λ$ is equal to the number of processes $n$ in the system, the $λ$-scanner object implements a multi-scanner object, while in case that $λ$ is equal to $1$, the $λ$-scanner object implements a single-scanner object. We present the $λ-Snap$ snapshot object, a wait-free $λ$-scanner snapshot implementation that has a step complexity of $O(λ)$ for $UPDATE$ operations and $O(λm)$ for $SCAN$ operat…
The well-known randomized consensus algorithm by Aspnes and Herlihy for asynchronous shared-memory systems was proved to work, even against a strong adversary, under the assumption that the registers that it uses are atomic registers. With atomic registers, every read or write operation is instantaneous (and thus indivisible). As pointed out by Golab et al. (2011), however, a randomized algorithm that works with atomic registers does not necessarily work if we replace the atomic registers that it uses with linearizable implementations of registers. This raises the following question: does the …
" Yet another paper on " the implementation of read/write registers in crash-prone asynchronous message-passing systems! Yes..., but, differently from its predecessors, this paper looks for a communication abstraction which captures the essence of such an implementation in the same sense that total order broadcast can be associated with consensus, or message causal delivery can be associated with causal read/write registers. To this end, the paper introduces a new communication abstraction, named SCD-broadcast (SCD standing for " Set Constrained Delivery "), which, instead of a single message,…
We present an algorithm for implementing a store-collect object in an asynchronous crash-prone message-passing dynamic system, where nodes continually enter and leave. The algorithm is very simple and efficient, requiring just one round trip for a store operation and two for a collect. We then show the versatility of the store-collect object for implementing churn-tolerant versions of useful data structures, while shielding the user from the complications of the underlying churn. In particular, we present elegant and efficient implementations of atomic snapshot and generalized lattice agreemen…
We present an approach for efficiently taking snapshots of the state of a collection of CAS objects. Taking a snapshot allows later operations to read the value that each CAS object had at the time the snapshot was taken. Taking a snapshot requires a constant number of steps and returns a handle to the snapshot. Reading a snapshotted value of an individual CAS object using this handle is wait-free, taking time proportional to the number of successful CASes on the object since the snapshot was taken. Our fast, flexible snapshots yield simple, efficient implementations of atomic multi-point quer…
In this paper, we describe a novel algorithm to create a con- current wait-free stack. To the best of our knowledge, this is the first wait-free algorithm for a general purpose stack. In the past, researchers have proposed restricted wait-free implementations of stacks, lock-free implementations, and efficient universal constructions that can support wait-free stacks. The crux of our wait-free implementation is a fast pop operation that does not modify the stack top; instead, it walks down the stack till it finds a node that is unmarked. It marks it but does not delete it. Subsequently, it is …
In this paper, we propose a generic concurrent directed graph (for shared memory architecture) that is concurrently being updated by threads adding/deleting vertices and edges. The graph is constructed by the composition of the well known concurrent list-based set data-structure from the literature. Our construction is generic, in the sense that it can be used to obtain various progress guarantees, depending on the granularity of the underlying concurrent set implementation - either blocking or non-blocking. We prove that the proposed construction is linearizable by identifying its linearizati…
This paper presents the first implementation of a search tree data structure in an asynchronous shared-memory system that provides a wait-free algorithm for executing range queries on the tree, in addition to non-blocking algorithms for Insert, Delete and Find, using single-word Compare-and-Swap (CAS). The implementation is linearizable and tolerates any number of crash failures. Insert and Delete operations that operate on different parts of the tree run fully in parallel (without any interference with one another). We employ a lightweight helping mechanism, where each Insert, Delete and Find…
We introduce a new shared memory object: the write-and-f-array, provide its wait-free implementation and use it to construct an improved wait-free implementation of the fetch-and-add object. The write-and-f-array generalizes single-writer write-and-snapshot object in a similar way that the f-array generalizes the multi-writer snapshot object. More specifically, a write-and-f-array is parameterized by an associative operator $f$ and is conceptually an array with two atomic operations: - write-and-f modifies a single array's element and returns the result of applying $f$ to all the elements, - r…
In classical asynchronous distributed systems composed of a fixed number n of processes where some proportion may fail by crashing, many objects do not have a wait-free linearizable implementation (e.g. stacks, queues, etc.). It has been proved that consensus is universal in such systems, which means that this system augmented with consensus objects allows to implement any object that has a sequential specification. To this end, many universal constructions have been proposed in systems augmented with consensus objects or with different equivalent objects or special hardware instructions (comp…
Atomic lock-free multi-word compare-and-swap (MCAS) is a powerful tool for designing concurrent algorithms. Yet, its widespread usage has been limited because lock-free implementations of MCAS make heavy use of expensive compare-and-swap (CAS) instructions. Existing MCAS implementations indeed use at least 2k+1 CASes per k-CAS. This leads to the natural desire to minimize the number of CASes required to implement MCAS. We first prove in this paper that it is impossible to "pack" the information required to perform a k-word CAS (k-CAS) in less than k locations to be CASed. Then we present the f…
Graph algorithms applied in many applications, including social networks, communication networks, VLSI design, graphics, and several others, require dynamic modifications -- addition and removal of vertices and/or edges -- in the graph. This paper presents a novel concurrent non-blocking algorithm to implement a dynamic unbounded directed graph in a shared-memory machine. The addition and removal operations of vertices and edges are lock-free. For a finite sized graph, the lookup operations are wait-free. Most significant component of the presented algorithm is the reachability query in a conc…
Adjacency lists are frequently used in graphing or map based applications. Although efficient concurrent linked-list algorithms are well known, it can be difficult to adapt these approaches to build a high-performance adjacency list. Furthermore, it can often be desirable to execute operations in these data structures transactionally, or perform a sequence of operations in one atomic step. In this paper, we present a lock-free transactional adjacency list based on a multi-dimensional list (MDList). We are able to combine known linked list strategies with the capability of the MDList in order t…
In this paper, we propose an efficient concurrent wait-free algorithm to construct an unbounded directed graph for shared memory architecture. To the best of our knowledge that this is the first wait-free algorithm for an unbounded directed graph where insertion and deletion of vertices and/or edges can happen concurrently. To achieve wait-freedom in a dynamic setting, threads help each other to perform the desired tasks using operator descriptors by other threads. To enhance performance, we also developed an optimized wait-free graph based on the principle of fast-path-slow-path. We also prov…
We describe a linearizable, wait-free implementation of a one-bit swap object from a single max register and an unbounded array of test-and-set bits. Each swap operation takes at most three steps. Using standard randomized constructions, the max register and test-and-set bits can be replaced by read-write registers, at the price of raising the cost of a swap operation to an expected O(max(log n, min(log t, n))) steps, where t is the number of times the swap object has previously changed its value and n is the number of processes.
The consensus number of an object is the maximum number of processes among which binary consensus can be solved using any number of instances of the object and read-write registers. Herlihy [6] showed in his seminal work that if an object has a consensus number of n, then there is a universal construction for a wait-free and linearizable implementation of any non-trivial concurrent object or data structure that is shared among n processes. Thus, a synchronization object such as compare-and-swap with an infinite consensus number and the corresponding instruction can be viewed as "strong". On th…
