Magnetic complex reluctance: Difference between revisions

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In [[computability theory]] and [[mathematical logic]] the '''Tarski–Kuratowski algorithm''' is a [[non-deterministic algorithm]] which provides an upper bound for the complexity of formulas in the [[arithmetical hierarchy]] and [[analytical hierarchy]].
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The algorithm is named after [[Alfred Tarski]] and [[Kazimierz Kuratowski]].
 
==Algorithm==
The Tarski–Kuratowski algorithm for the arithmetical hierarchy:
# Convert the formula to [[prenex normal form]].
# If the formula is quantifier-free, it is in <math>\Sigma^0_0</math> and <math>\Pi^0_0</math>.
# Otherwise, count the number of alternations of quantifiers; call this ''k''.
# If the first quantifier is [[Existential quantification|∃]], the formula is in <math>\Sigma^0_{k+1}</math>.
# If the first quantifier is [[Universal quantification|∀]], the formula is in <math>\Pi^0_{k+1}</math>.
 
==References==
*Rogers, H. ''The Theory of Recursive Functions and Effective Computability'', MIT Press. ISBN 0-262-68052-1; ISBN 0-07-053522-1
 
{{DEFAULTSORT:Tarski-Kuratowski algorithm}}
[[Category:Mathematical logic hierarchies]]
[[Category:Computability theory]]
[[Category:Theory of computation]]
 
 
{{mathlogic-stub}}

Latest revision as of 23:05, 16 October 2014

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