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Tarski–Kuratowski algorithm
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Tarski–Kuratowski algorithm : ウィキペディア英語版
Tarski–Kuratowski algorithm
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.
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 \Sigma^0_0 and \Pi^0_0.
# Otherwise, count the number of alternations of quantifiers; call this ''k''.
# If the first quantifier is , the formula is in \Sigma^0_.
# If the first quantifier is , the formula is in \Pi^0_.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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