Registers

Consider a system of asynchronous processes that communicate among themselves by only executing read and write operations on a set of shared variables (also known as shared registers). The system has no global clock or other synchronization primitives. Every shared variable is associated with a process (called owner) which writes it and the other processes may read it. An execution of a write (read) operation on a shared variable will be referred to as a Write (Read) on that variable. A Write on a shared variable puts a value from a predetermined finite domain into the variable, and a Read reports a value from the domain. A process that writes (reads) a variable is called a writer (reader) of the variable. We want to construct shared variables in which the following two properties hold. (1) Operation executions are not necessarily atomic, that is, they are not indivisible but rather consist of atomic sub-operations, and (2) every operation finishes its execution within a bounded number of its own steps, irrespective of the presence of other operation executions and their relative speeds. That is, operation executions are wait-free. These two properties give rise to a classification of shared variables, depending on their output characteristics. Lamport [8] distinguishes three categories for 1-writer shared variables, using a precedence relation on operation executions defined as follows: for operation executions A and B, A precedes B, denoted A −→ B, if A finishes before B starts; A and B overlap if neither A precedes B nor B precedes A. In 1-writer variables, all the Writes are totally ordered by " −→ ". The three categories of 1-writer shared variables defined by Lamport are the following. 1. A safe variable is one in which a Read not overlapping any Write returns the most recently written value. A Read that overlaps a Write may return any value from the domain of the variable.