A wait-free implementation of a concurrent data object is one that guarantees that any process can complete any operation in a finite number of steps, regardless of the execution speeds of the other processes. The problem of constructing a wait-free implementation of one data object from another lies at the heart of much recent work in concurrent algorithms, concurrent data structures, and multiprocessor architectures. In the first part of this paper, we introduce a simple and general technique, based on reduction to a consensus protocol, for proving statements of the form "there is no wait-free implementation of X by Y ." We derive a hierarchy of objects such that no object at one level has a wait-free implementation in terms of objects at lower levels. In particular, we show that atomic read/write registers, which have been the focus of much recent attention, are at the bottom of the hierarchy: they cannot be used to construct wait-free implementations of many simple and familiar da...

A con.curren.t object is a data structure shared by concurrent processes. Conventional techniques for implementing concurrent objects typically rely on criticaI sections: ensuring that only one process at a time can operate on the object. Nevertheless, critical sections are poorly suited for asynchronous systems: if one process is halted or delayed in a critical section, other, non-faulty processes will be unable to progress. By contrast, a concurrent object implementation is non-blocking if it always guarantees that some process will complete an operation in a finite number of steps, and it is wait-free if it guarantees that each process will complete an operation in a finite number of steps. This paper proposes a new methodology for constructing non-blocking aud wait-free implementations of concurrent objects. The object’s representation and operations are written as st,ylized sequential programs, with no explicit synchronization. Each sequential operation is automatically transformed into a non-blocking or wait-free operation usiug novel synchronization and memory management algorithms. These algorithms are presented for a multiple instruction/multiple data (MIM D) architecture in which n processes communicate by applying read, write, and comparekYswa,p operations to a shared memory. 1

We give a new randomized algorithm for achieving consensus among asynchronous processes that communicate by reading and writing shared registers. The fastest previously known algorithm has exponential expected running time. Our algorithm is polynomial, requiring an expected O(n 4 ) operations. Applications of this algorithm include the elimination of critical sections from concurrent data structures and the construction of asymptotically unbiased shared coins.

We introduce a shared data object, called a composite register, that generalizes the notion of an atomic register. A composite register is an array-like shared data object that is partitioned into a number of components. An operation of a composite register either writes a value to a single component or reads the values of all components. A composite register reduces to an ordinary atomic register when there is only one component. In this paper, we show that multi-reader, single-writer atomic registers can be used to implement a composite register in which there is only one writer per component. In a related paper, we show how to use the composite register construction of this paper to implement a composite register with multiple writers per component. These two constructions show that it is possible to implement a shared memory that can be read in its entirety in a single snapshot operation, without using mutual exclusion. Keywords: atomicity, atomic register, composite register, conc...

In the asynchronous PRAM model, processes communicate by atomically reading and writing shared memory locations. This paper investigates the extent to which asynchronous PRAM permits long-lived, highly concurrent data structures. An implementation of a concurrent object is wait-free if every operation will complete in a finite number of steps, and it is k-bounded wait-free, for some k > 0, if every operation will complete within k steps. In the first part of this paper, we show that there are objects with wait-free implementations but no k-bounded wait-free implementations for any k, and that there is an infinite hierarchy of objects with implementations that are k-bounded wait-free but not K-bounded wait-free for some K > k. In the second part of the paper, we give an algebraic characterization of a large class of objects that do have wait-free implementations in asynchronous PRAM, as well as a general algorithm for implementing them. Our tools include simple iterative algorithms for wait-free approximate agreement and atomic snapshot.

We introduce concurrent time-stamping, a paradigm that allows processes to temporally order concurrent events in an asynchronous shared-memory system. Concurrent time-stamp systems are powerful tools for concurrency control, serving as the basis for solutions to coordination problems such as mutual exclusion, l-exclusion, randomized consensus, and multiwriter multireader atomic registers. Unfortunately, all previously known methods for implementing concurrent timestamp systems have been theoretically unsatisfying since they require unbounded-size time-stamps -- in other words, unbounded-size memory. This work presents the first bounded implementation of a concurrent time-stamp system, providing a modular unbounded-to-bounded transformation of the simple unbounded solutions to problems such as those mentioned above. It allows solutions to two formerly open problems, the boundedprobabilistic -consensus problem of Abrahamson and the fifo-l-exclusion problem of Fischer, Lynch, Burns and...

This work aims to establish the viability of lock-free object sharing in uniprocessor real-time systems. Naive usage of conventional lock-based object-sharing schemes in real-time systems leads to unbounded priority inversion. A priority inversion occurs when a task is blocked by a lower-priority task that is inside a critical section. Mechanisms that bound priority inversion usually entail kernel overhead that is sometimes excessive. We propose that lock-free objects offer an attractive alternative to lock-based schemes because they eliminate priority inversion and its associated problems. On the surface, lock-free objects may seem to be unsuitable for hard real-time systems because accesses to such objects are not guaranteed to complete in bounded time. Nonetheless, we present scheduling conditions that demonstrate the applicability of lock-free objects in hard real-time systems. Our scheduling conditions are applicable to schemes such as rate-monotonic scheduling and earliest-deadline-...

We define a class of operations called pseudo read-modify-write (PRMW) operations, and show that nontrivial shared data objects with such operations can be implemented in a bounded, wait-free manner from atomic registers. A PRMW operation is similar to a "true" read-modify-write (RMW) operation in that it modifies the value of a shared variable based upon the original value of that variable. However, unlike an RMW operation, a PRMW operation does not return the value of the variable that it modifies. We consider a class of shared data objects that can either be read, written, or modified by an associative, commutative PRMW operation, and show that any object in this class can be implemented without waiting from atomic registers. The implementations that we present are polynomial in both space and time and thus are an improvement over previously published ones, all of which have unbounded space complexity. Keywords: assertional reasoning, atomicity, atomic register, composite register, ...

Shared registers are basic objects used as communication mediums in asynchronous concurrent computation. A concurrent timestamp system is a higher typed communication object, and has been shown to be a powerful tool to solve many concurrency control problems. It has turned out to be possible to construct such higher typed objects from primitive lower typed ones. The next step is to find efficient constructions. We propose a very efficient wait-free construction of bounded concurrent timestamp systems from 1-writer shared registers. This finalizes, corrects, and extends a preliminary bounded multiwriter construction proposed by the second author in 1986. That work partially initiated the current interest in wait-free concurrent objects, and introduced a notion of discrete vector clocks in distributed algorithms.

Agreement problems are central to the study of wait-free protocols for shared memory distributed systems. We examine two specific issues arising out of this study. We consider the complexity of the wait-free approximate agreement problem in an asynchronous shared memory comprised of only single-bit multi-writer multi-reader registers. For real-valued inputs of magnitude at most s and a real-valued accuracy requirement " ? 0 we show matching upper and lower bounds of \Theta(log(s=")) steps and shared registers. For inputs drawn from any fixed finite range this is significantly better than the best possible algorithm for single-writer multi-reader registers, which, for n processes, requires \Omega\Gammaire n) steps. These results are used to show a separation between the wait-free single-writer mult...