Space and time constructible functions. Why do I care? CS 611. announcements. No office hours tommorow. Qualifying exam policy is out. you can choose Schedule changes posted on blog. Space Constructible. A function S( n ) is space constructible if…
Why do I care?
“For every space bound t(n), all TMs with space bound g(n) such that g(n) > t(n) can solve more problems than TMs with space bound t(n)”
(i.e., more time always gives more power)
Example: suppose t(n) = sin(n). Then DTIME(sin(n)) = DTIME(22^sin(n))
If s1(n) in o(s2(n)) then
DTIME(s1) subset DTIME (s2).
(theorem 5.15 in our book).
f(n)*g(n), 2f(n) and f(n)g(n)
are space constructible too.
(for fully space constructible S(n), of course).