Almost Optimal Single Reader, Single Writer Atomic Register

Abstract

Lamport defined three classes of communication registers: safe, regular, and atomic. Wait-free implementations of one register class from a weaker class abound in the literature. However, results establishing the intrinsic complexity of such implementations are relatively scarce. In this paper, we consider the problem of implementing an n-valued single reader, single writer atomic register A from two regular registers, BUF and R, where BUF is a regular register that only the writer of A can write and R is a regular register that only the reader of A can write. (Lamport proved that there cannot be an implementation without R, so R is at least 2-valued in any implementation.) We present an almost space optimal implementation. Specifically, our results are: (1) An implementation for which BUF is 2n-valued and R is 2-valued; and (2) A lower bound stating that, in any implementation, regardless of how large R is, BUF must be at least (2n−1)-valued.