Randomized protocols for asynchronous consensus

The famous Fischer, Lynch, and Paterson impossibility proof shows that it is impossible to solve the consensus problem in a natural model of an asynchronous distributed system if even a single process can fail. Since its publication, two decades of work on fault-tolerant asynchronous consensus algorithms have evaded this impossibility result by using extended models that provide (a) randomization, (b) additional timing assumptions, (c) failure detectors, or (d) stronger synchronization mechanisms than are available in the basic model. Concentrating on the first of these approaches, we illustrate the history and structure of randomized asynchronous consensus protocols by giving detailed descriptions of several such protocols.Comment: 29 pages; survey paper written for PODC 20th anniversary issue of Distributed Computin

Generic Proofs of Consensus Numbers for Abstract Data Types

The power of shared data types to solve consensus in asynchronous wait-free systems is a fundamental question in distributed computing, but is largely considered only for specific data types. We consider general classes of abstract shared data types, and classify types of operations on those data types by the knowledge about past operations that processes can extract from the state of the shared object. We prove upper and lower bounds on the number of processes which can use data types in these classes to solve consensus. Our results generalize the consensus numbers known for a wide variety of specific shared data types, such as compare-and-swap, augmented queues and stacks, registers, and cyclic queues. Further, since the classification is based directly on the semantics of operations, one can use the bounds we present to determine the consensus number of a new data type from its specification. We show that, using sets of operations which can detect the first change to the shared object state, or even one at a fixed distance from the beginning of the execution, any number of processes can solve consensus. However, if instead of one of the first changes, operations can only detect one of the most recent changes, then fewer processes can solve consensus. In general, if each operation can either change shared state or read it, but not both, then the number of processes which can solve consensus is limited by the number of consecutive recent operations which can be viewed by a single operation. Allowing operations that both change and read the shared state can allow consensus algorithms with more processes, but if the operations can only see one change a fixed number of operations in the past, we upper bound the number of processes which can solve consensus with a small constant

Consensus Numbers of Multi-Objects

This paper studies the ability of shared memory distributed systems to solve the wait-free consensus problem if processes are permitted to access more than one shared data object in a single atomic action. Suppose T is any deterministic object type that can be used, with read/write registers, to solve consensus among n processes, with n ? 2. A multiobject of type T m consists of a collection of objects of type T , any m of which can be accessed in a single atomic action. It will be shown that a multi-object of type T m can be used, with registers, to solve consensus among\Omega\Gamma n p m) processes. Furthermore, if the type T is equipped with operations that allow processes to read its state without altering the state, then the multi-object can be used with registers to solve consensus among \Omega\Gamma nm) processes. Neither of these lower bounds can be improved. 1 Introduction In a shared memory distributed system, processes communicate by accessing shared data objects..