Register machine

In mathematical logic and theoretical computer science a register machine is a generic class of abstract machines used in a manner similar to a Turing machine. All the models are Turing equivalent.

The register machine gets its name from its use of one or more "registers". In contrast to the tape and head used by a Turing machine, the model uses multiple, uniquely addressed registers, each of which holds a single positive integer.

There are at least 4 sub-classes found in literature, here listed from most primitive to the most like a computer:

Any properly defined register machine model is Turing equivalent. Computational speed is very dependent on the model specifics.

In practical computer science, a similar concept known as a virtual machine is sometimes used to minimise dependencies on underlying machine architectures. Such machines are also used for teaching. The term "register machine" is sometimes used to refer to a virtual machine in textbooks.

A register machine consists of:

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).

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