Consistency, optimality, and incompleteness
نویسندگان
چکیده
منابع مشابه
Consistency, optimality, and incompleteness
Assume that the problem P0 is not solvable in polynomial time. Let T be a first-order theory containing a sufficiently rich part of true arithmetic. We characterize T∪{ConT } as the minimal extension of T proving for some algorithm that it decides P0 as fast as any algorithm B with the property that T proves that B decides P0. Here, ConT claims the consistency of T . As a byproduct, we obtain a...
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Assume that the problem Q0 is not solvable in polynomial time. For theories T containing a sufficiently rich part of true arithmetic we characterize T ∪ {ConT } as the minimal extension of T proving for some algorithm that it decides Q0 as fast as any algorithm B with the property that T proves that B decides Q0. Here, ConT claims the consistency of T . Moreover, we characterize problems with a...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2013
ISSN: 0168-0072
DOI: 10.1016/j.apal.2013.06.009