Historical Development of The Register Machine Model
Two trends appeared in the early 1950s—the first to characterize the computer as a Turing machine, the second to define computer-like models—models with sequential instruction sequences and conditional jumps—with the power of a Turing machine, i.e. a so-called Turing equivalence. Need for this work was carried out in context of two "hard" problems: the unsolvable word problem posed by Emil Post—his problem of "tag"—and the very "hard" problem of Hilbert's problems—the 10th question around Diophantine equations. Researchers were questing for Turing-equivalent models that were less "logical" in nature and more "arithmetic" (cf Melzak (1961) p. 281, Shepherdson-Sturgis (1963) p. 218).
The first trend—toward characterizing computers—seems to have originated with Hans Hermes (1954), Rózsa Péter (1958), and Heinz Kaphengst (1959), the second trend with Hao Wang (1954, 1957) and, as noted above, furthered along by Zdzislaw Alexander Melzak (1961), Joachim Lambek (1961), Marvin Minsky (1961, 1967), and John Shepherdson and Howard E. Sturgis (1963).
The last five names are listed explicitly in that order by Yuri Matiyasevich. He follows up with:
- "Register machines are particularly suitable for constructing Diophantine equations. Like Turing machines, they have very primitive instructions and, in addition, they deal with numbers" (Yuri Matiyasevich (1993), Hilbert's Tenth Problem, commentary to Chapter 5 of the book, at http://logic.pdmi.ras.ru/yumat/H10Pbook/commch_5htm. )
It appears that Lambek, Melzak, Minsky and Shepherdson and Sturgis independently anticipated the same idea at the same time. See Note On Precedence below.
The history begins with Wang's model.
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