Register Machine - Precedence

Precedence

Minsky was working at the M.I.T. Lincoln Labs and published his work there; his paper was received for publishing in the Annals of Mathematics on August 15, 1960 but not published until November 1961. While receipt occurred a full year before the work of Melzak and Lambek was received and published (received, respectively, May and June 15, 1961 and published side-by-side September 1961). That (i) both were Canadians and published in the Canadian Mathematical Bulletin, (ii) neither would have had reference to Minsky's work because it was not yet published in a peer-reviewed journal, but (iii) Melzak references Wang, and Lambek references Melzak, leads one to hypothesize that their work occurred simultaneously and independently.

Almost exactly the same thing happened to Shepherdson and Sturgis. Their paper was received in December 1961—just a few months after Melzak and Lambek's work was received. Again, they had little (at most 1 month) or no benefit of reviewing the work of Minsky. They were careful to observe in footnotes that papers by Ershov, Kaphengst and Peter had "recently appeared" (p. 219). These were published much earlier but appeared in the German language in German journals so issues of accessibility present themselves.

The final paper of Shepherdson and Sturgis did not appear in a peer-reviewed journal until 1963. And as they fairly and honestly note in their Appendix A, the 'systems' of Kaphengst (1959), Ershov (1958), Peter (1958) are all so similar to what results were obtained later as to be indistinguishable to a set of the following:

produce 0 i.e. 0 --> n

increment a number i.e. n+1 --> n

"i.e. of performing the operations which generate the natural numbers" (p. 246)

copy a number i.e. n --> m

to "change the course of a computation", either comparing two numbers or decrementing until 0

Indeed, Shepherson and Sturgis conclude

"The various minimal systems are very similar"( p. 246)

By order of publishing date the work of Kaphengst (1959), Ershov (1958), Peter (1958) were first. Does context matter? An answer would require close examination of the papers. Conclusions and opinions about this will be left to the reader.