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 describe a new architecture for Byzantine fault tolerant state machine replication that separates agreement that orders requests from execution that processes requests. This separation yields two fundamental and practically significant advantages over previous architectures. First, it reduces replication costs because the new architecture can tolerate faults in up to half of the state machine replicas that execute requests. Previous systems can tolerate faults in at most a third of the combined agreement/state machine replicas. Second, separating agreement from execution allows a general privacy firewall architecture to protect confidentiality through replication. In contrast, replication in previous systems hurts confidentiality because exploiting the weakest replica can be su#cient to compromise the system. We have constructed a prototype and evaluated it running both microbenchmarks and an NFS server. Overall, we find that the architecture adds modest latencies to unreplicated systems and that its performance is competitive with existing Byzantine fault tolerant systems.

We give necessary and sufficient combinatorial conditions characterizing the computational tasks that can be solved by N asynchronous processes, up to t of which can fail by halting. The range of possible input and output values for an asynchronous task can be associated with a high-dimensional geometric structure called a simplicial complex. Our main theorem characterizes computability y in terms of the topological properties of this complex. Most notably, a given task is computable only if it can be associated with a complex that is simply connected with trivial homology groups. In other words, the complex has “no holes!” Applications of this characterization include the first impossibility results for several long-standing open problems in distributed computing, such as the “renaming ” problem of Attiya et. al., the “k-set agreement ” problem of Chaudhuri, and a generalization of the approximate agreement problem. 1

We give necessary and sufficient combinatorial conditions characterizing the tasks that can be solved by asynchronous processes, of which all but one can fail, that communicate by reading and writing a shared memory. We introduce a new formalism for tasks, based on notions from classical algebraic and combinatorial topology, in which a task's possible input and output values are each associated with high-dimensional geometric structures called simplicial complexes. We characterize computability in terms of the topological properties of these complexes. This characterization has a surprising geometric interpretation: a task is solvable if and only if the complex representing the task's allowable inputs can be mapped to the complex representing the task's allowable outputs by a function satisfying certain simple regularity properties. Our formalism thus replaces the "operational" notion of a wait-free decision task, expressed in terms of interleaved computations unfolding ...

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.

Most complexitymeasures for concurrent algorithms for asynchronous sharedmemory architectures focus on process steps and memory consumption. In practice, however, performance of multiprocessor algorithms is heavily influenced by contention, the extent to which processes access the same location at the same time. Nevertheless, even though contention is one of the principal considerations affecting the performance of real algorithms on real multiprocessors, there are no formal tools for analyzing the contention of asynchronous shared-memory algorithms. This paper introduces the first formal complexity model for contention in multiprocessors. We focus on the standard multiprocessor architecture in which n asynchronous processes communicate by applying read, write, and read-modify-write operations to a shared memory. We use our model to derive two kinds of results: (1) lower bounds on contention for well known basic problems such as agreement and mutual exclusion, and (2) trade-offs betwe...

A protocol is presented which solves the randomized consensus problem[9] for shared memory. The protocol uses a total of O(p 2 +n) worst-case expected increment, decrement and read operations on a set of three shared O(logn)-bit counters, where p is the number of active processors and n is the total number of processors. It requires less space than previous polynomial-time consensus protocols[6, 7], and is faster when not all of the processors participate in the protocol. A modified version of the protocol yields a weak shared coin whose bias is guaranteed to be in the range 1=2 \Sigma ffl regardless of scheduler behavior, and which is the first such protocol for the shared-memory model to guarantee that all processors agree on the outcome of the coin. 1 1.

Probability features increasingly often in software and hardware systems: it is used in distributed co-ordination and routing problems, to model fault-tolerance and performance, and to provide adaptive resource management strategies. Probabilistic model checking is an automatic procedure for establishing if a desired property holds in a probabilistic model, aimed at verifying probabilistic specifications such as "leader election is eventually resolved with probability 1", "the chance of shutdown occurring is at most 0.01%", and "the probability that a message will be delivered within 30ms is at least 0.75". A probabilistic model checker calculates the probability of a given temporal logic property being satisfied, as opposed to validity. In contrast to conventional model checkers, which rely on reachability analysis of the underlying transition system graph, probabilistic model checking additionally involves numerical solutions of linear equations and linear programming problems. This paper reports our experience with implementing PRISM (www.cs.bham.ac.uk/dxp/ prism/), a Probabilistic Symbolic Model Checker, demonstrates its usefulness in analysing real-world probabilistic protocols, and outlines future challenges for this research direction.