Canadian Mathematical Bulletin · 1961 · 20 citations · 2 references
ComputingComputer ScienceMathematicsNumber TheorySet TheoryTheory Of ComputationComputability TheoryTuring MachinesComputabilityEffective ComputabilityTuring Machine ComputabilityTuring Machine Model
Turing’s 1936 work formalized effective computability, aiming to separate numbers defined by existential statements from those defined constructively. He modeled computation with an A‑machine—a box with an infinite tape of symbols, one square in the box at a time, advancing in discrete steps.
In 1936 A. M. Turing published his analysis of the notion of effective computability. Very roughly speaking, its object was to distinguish between numbers defined by existential statements and those defined by purely constructive ones. Guided by his schematizing of what goes on when a person calculates using paper and pencil, Turing introduced the concept of an A-machine, eventually to be called a Turing machine. Such a machine consists of a box and a linear tape divided into squares, indefinitely long in both directions. The tape passes through the box and exactly one square of it is always within the box. The system changes only at certain discrete times: t = 0, 1, …. Each square can carry exactly one of the finite set of symbols: s 1 , s 2 , …, s n , one of which may be the blank.
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An Introduction to Diophantine Approximation.
John C. Brixey, J. W. S. Cassels · American Mathematical Monthly · 1958 · 1.2K citations