Ackermann function: Difference between revisions
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imported>Dmitrii Kouznetsov (copypast the preamble from wikipedia.) |
imported>Dmitrii Kouznetsov (<references/>) |
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In [[computability theory]], the '''Ackermann function''' or '''Ackermann-Péter function''' is a simple example of a [[computable function]] that is not [[Primitive recursive function|primitive recursive]]. The set of primitive recursive functions is a [[subset]] of the set of general recursive functions. Ackermann's function is an example that shows that the former is a [[strict subset]] of the latter. | In [[computability theory]], the '''Ackermann function''' or '''Ackermann-Péter function''' is a simple example of a [[computable function]] that is not [[Primitive recursive function|primitive recursive]]. The set of primitive recursive functions is a [[subset]] of the set of general recursive functions. Ackermann's function is an example that shows that the former is a [[strict subset]] of the latter. | ||
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Its value grows rapidly; even for small inputs, for example A(''4,2'') contains 19,729 decimal digits <ref>[http://www.kosara.net/thoughts/ackermann42.html Decimal expansion of A(4,2)]</ref>. | Its value grows rapidly; even for small inputs, for example A(''4,2'') contains 19,729 decimal digits <ref>[http://www.kosara.net/thoughts/ackermann42.html Decimal expansion of A(4,2)]</ref>. | ||
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Revision as of 07:22, 8 November 2008
In computability theory, the Ackermann function or Ackermann-Péter function is a simple example of a computable function that is not primitive recursive. The set of primitive recursive functions is a subset of the set of general recursive functions. Ackermann's function is an example that shows that the former is a strict subset of the latter.
The Ackermann function is defined recursively for non-negative integers m and n as follows::
Its value grows rapidly; even for small inputs, for example A(4,2) contains 19,729 decimal digits [1].