Unformatted text preview: PSPACE . 2. Show that one of the following inequalities must hold: L ̸ = P or P ̸ = PSPACE . Note that both are believed to be true, and no one knows how to prove either one is true. 3. Show that logspace reductions are closed under composition. Then use the same ideas to prove that if language A is P-complete, then A ∈ L implies L = P . 4. Use a padding argument to show that if L = P then PSPACE = EXP . 5. Prove that SPACE( O ( n ) ) ̸ = P . (Note that while this is an interesting result, it doesn’t seem to shed any light on the major open questions L ? = P and P ? = PSPACE ). Hint: consider a language A and a padded version of A . How are the two languages related with respect to space? How are they related with respect to time? 1-1...
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- Fall '09
- Computational complexity theory, PSPACE, major open questions, downward self-reducible language, polynomial time procedure