von Neumann architecture
<architecture, computability> A computer architecture conceived by
mathematician John von Neumann, which forms the core of nearly every computer
system in use today (regardless of size). In contrast to a Turing machine, a von
Neumann machine has a random-access memory (RAM) which means that each
successive operation can read or write any memory location, independent of the
location accessed by the previous operation.
A von Neumann machine also has a central processing unit (CPU) with one or more
registers that hold data that are being operated on. The CPU has a set of
built-in operations (its instruction set) that is far richer than with the
Turing machine, e.g. adding two binary integers, or branching to another part of
a program if the binary integer in some register is equal to zero (conditional
branch).
The CPU can interpret the contents of memory either as instructions or as data
according to the fetch-execute cycle.
Von Neumann considered parallel computers but recognized the problems of
construction and hence settled for a sequential system. For this reason,
parallel computers are sometimes referred to as non-von Neumann architectures.
A von Neumann machine can compute the same class of functions as a universal
Turing machine.
[Reference? Was von Neumann's design, unlike Turing's, originally intended for
physical implementation?]
http://www.salem.mass.edu/~tevans/VonNeuma.htm.
(2003-05-16)
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von Neumann integer
<mathematics> A finite von Neumann ordinal.
The von Neumann integer N is a finite set with N elements which are the von
Neumann integers 0 to N-1. Thus
0 = {} = {}
1 = {0} = {{}}
2 = {0, 1} = {{}, {{}}}
3 = {0, 1, 2} = {{}, {{}}, {{}, {{}}}}
...
The set of von Neumann integers is infinite, even though each of its
elements is finite.
[Origin of name?]
(1995-03-30)
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von Neumann, John
John von Neumann
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Volume Table Of Contents « von Neumann architecture
« von Neumann integer « von Neumann, John »
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von Neumann machine
von Neumann architecture
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Neumann, John « von Neumann machine » von
Neumann ordinal » voodoo programming » Voronoi
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von Neumann ordinal
<mathematics> An implementation of ordinals in set theory (e.g. Zermelo
Fränkel set theory or ZFC). The von Neumann ordinal alpha is the well-ordered
set containing just the ordinals "shorter" than alpha.
"Reasonable" set theories (like ZF) include Mostowski's Collapsing Theorem: any
well-ordered set is isomorphic to a von Neumann ordinal. In really screwy
theories (e.g. NFU -- New Foundations with Urelemente) this theorem is false.
The finite von Neumann ordinals are the von Neumann integers.
(1995-03-30)
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