 
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 "speedup lemma" and a
"slowdown lemma" using the power of alternations to prove the above theorems.
