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Summary: Com S 631: Lower bounds and Separation Results
Lecture 3 Scribe: Debasis Mandal
1. Time/Space tradeoff for SAT
We don't know whether SAT can be solved in polynomial time or linear space in determin-
istic machine. However, we know that SAT can not be solved simultaneously in polynomial
time and polylog space in a deterministic machine. In particular, we know
Theorem 1. SAT TISP(nc
, log n) if c <
2.
To start with, we prove the following theorem and then get the above result as a straight-
forward corollary.
Theorem 2. NTIME(n) TISP(nc
, log2
n) if c <
2.
We assume that t(n) is a time constructible function and s(n) is a space constructible
function on input size n. As stated in the last lecture, we prove a "speed-up lemma" and a
"slow-down lemma" using the power of alternations to prove the above theorems.
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