Difference between revisions of "Recursive predicate"
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| + | $#C+1 = 3 : ~/encyclopedia/old_files/data/R080/R.0800300 Recursive predicate | ||
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| + | A [[Predicate|predicate]] $ P( x _ {1} \dots x _ {n} ) $ | ||
| + | defined on the natural numbers, such that the function $ f $ | ||
| + | defined on the natural numbers by the condition | ||
| + | |||
| + | $$ | ||
| + | f( x _ {1} \dots x _ {n} ) = \left \{ | ||
| + | |||
| + | \begin{array}{ll} | ||
| + | 1 & \textrm{ if } P( x _ {1} \dots x _ {n} ) \textrm{ is true }, \\ | ||
| + | 0 & \textrm{ if } P( x _ {1} \dots x _ {n} ) \textrm{ is false } , \\ | ||
| + | \end{array} | ||
| + | |||
| + | \right .$$ | ||
is a [[Recursive function|recursive function]]. | is a [[Recursive function|recursive function]]. | ||
Latest revision as of 14:55, 7 June 2020
A predicate $ P( x _ {1} \dots x _ {n} ) $
defined on the natural numbers, such that the function $ f $
defined on the natural numbers by the condition
$$ f( x _ {1} \dots x _ {n} ) = \left \{ \begin{array}{ll} 1 & \textrm{ if } P( x _ {1} \dots x _ {n} ) \textrm{ is true }, \\ 0 & \textrm{ if } P( x _ {1} \dots x _ {n} ) \textrm{ is false } , \\ \end{array} \right .$$
is a recursive function.
How to Cite This Entry:
Recursive predicate. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Recursive_predicate&oldid=49395
Recursive predicate. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Recursive_predicate&oldid=49395
This article was adapted from an original article by V.E. Plisko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article