On Jul 6, 2010, at 12:23 AM, Steffen Schuldenzucker wrote:
Given the definition of a recursive function f in, say, haskell,
determine if f can be implemented in O(1) memory.
How are you supposed to handle integer arithmetic?
If you don't take the size of integers into account,
then since a Turing machine can do any computation,
it can run a Haskell interpreter, and since a Turing
machine's tape can be modelled by a single integer
(or more conveniently by two), any Haskell function
can be implemented in O(1) Integers.
If you do take the size of integers into account,
then
pow2 n = loop n 1
where loop 0 a = a
loop (m+1) a = loop m (a+a)
requires O(n) memory.
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