Most computer scientists regard synchronization problems, such as the mutual exclusion problem, to be problems of mathematics. How can you use one class of mathematical objects, like atomic reads and writes, to implement some other mathematical object, like a mutual exclusion algorithm? I have always regarded synchronization problems to be problems of physics. How do you use physical objects, like registers, to achieve physical goals, like not having two processes active at the same time?
With the discovery of the bakery algorithm (see ), I began considering the question of how two processes communicate. I came to the conclusion that asynchronous communication requires some object whose state can be changed by one process and observed by the other. We call such an object a register. This paper introduced three classes of registers. The weakest class with which arbitrary synchronization is possible is called safe. The next strongest is called regular and the strongest, generally assumed by algorithm writers, is called atomic.
I had obtained all the results presented here in the late 70s and had described them to a number of computer scientists. Nobody found them interesting, so I never wrote them up. Around 1984, I saw a paper by Jay Misra, motivated by VLSI, that was heading in the general direction of my results. It made me realize that, because VLSI had started people thinking about synchronization from a more physical perspective, they might now be interested in my results about registers. So, I wrote this paper. As with [61a][61b], the first part describes my formalism for describing systems with nonatomic operations. This time, people were interested–perhaps because it raised the enticing unsolved problem of implementing multi-reader and multi-writer atomic registers. It led to a brief flurry of atomic register papers.
Fred Schneider was the editor who processed this paper. He kept having trouble understanding the proof of my atomic register construction. After a couple of rounds of filling in the details of the steps that Schneider couldn’t follow, I discovered that the algorithm was incorrect. Fortunately, I was able to fix the algorithm and write a proof that he, I, and, as far as I know, all subsequent readers did believe.
Some fifteen years later, Jerry James, a member of the EECS department at the University of Kansas, discovered a small error in Proposition 1 when formalizing the proofs with the PVS mechanical verification system. He proved a corrected version of the proposition and showed how that version could be used in place of the original one. A pdf file containing a note by James describing the error and its correction can be viewed under the ‘Related Items’ tab.