Pi is in Log Space
نویسنده
چکیده
We say that a real number α is in Log space if its n-th bit (n ∈ Z) can be computed in O(log |n|) space. We show that π = 3.14159 · · · is in Log space. This implies that π is in the complexity class SC. The latter result has been conjectured by Lipton, and widely assumed to be true from the work of Bailey, Borwein and Plouffe (BBP) and others. Our result extends to other constants such as log 2 or π that also possess two essential ingredients: they have BBP-like series and have bounded irrationality measures.
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