Some results on the impossibility, universality, and decidability of consensus

Abstract

A concurrent system consists of processes communicating via shared objects. Examples of shared object types include data structures such as r e g i s t e r , queue, and t r ee , and synchronization primitives such as t e s t ~ s e t , and compaxe~suap. Even though different processes may concurrently access a shared object, the object must behave as if all these accesses occur in some sequential order. More precisely, the behavior of a shared object must be linearizable [9]. One way to ensure linearizability is to implement shared objects using critical sections [5]. This approach, however, is not fault-tolerant: The crash of a process while in the critical section of a shared object can permanently prevent the rest of the processes from accessing that object. This lack of fault-tolerance led to the concept of wait-free implementations of shared objects [11, 16, 7]. Informally, an implementation of a shared object is wait-free if every process can complete every operation on that object in a finite number of its own steps, regardless of the execution speeds of the remaining processes. Thus, a concurrent system in which all implementations of shared objects are wait-free is resilient to process crashes. Most implementations in the literature build complex registers from simpler ones [1, 2, 3, 10, 12, 14, 16, 15, 18, 19, 20, 21], while the others are related to consensus objects [13, 4]. The bigger picture emerged when Herlihy discovered a close connection between wait-free implementations and objects of a particular type called cons ensus 1. In [7], he presented a "universal" construction that transforms the sequential implementation of an object into a wait-free concurrent implementation using only consensus objects and registers. He also showed that analysing primitives in terms of their ability to implement consensus objects helps order primitives