کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
438586 | 690296 | 2007 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Turing’s unpublished algorithm for normal numbers
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موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In an unpublished manuscript, Alan Turing gave a computable construction to show that absolutely normal real numbers between 0 and 1 have Lebesgue measure 1; furthermore, he gave an algorithm for computing instances in this set. We complete his manuscript by giving full proofs and correcting minor errors. While doing this, we recreate Turing’s ideas as accurately as possible. One of his original lemmas remained unproved, but we have replaced it with a weaker lemma that still allows us to maintain Turing’s proof idea and obtain his result.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Theoretical Computer Science - Volume 377, Issues 1–3, 31 May 2007, Pages 126-138
Journal: Theoretical Computer Science - Volume 377, Issues 1–3, 31 May 2007, Pages 126-138