lec18 - CS151 Complexity Theory Course Summary Lecture 18...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 CS151 Complexity Theory Lecture 18 May 26, 2011 May 26, 2011 2 Course Summary May 26, 2011 3 Course summary • Time and space – hierarchy theorems – FVAL in L – CVAL P -complete – QSAT PSPACE -complete – succinct CVAL EXP -complete May 26, 2011 4 Course summary • Non-determinism – NTIME hierarchy theorem – “NP-intermediate” problems (Ladner’s Theorem) – unary languages (likely) not NP-complete – Savitch’s Theorem – Immerman-Szelepcsényi Theorem Problem sets: sparse languages (likely) not NP-complete May 26, 2011 5 Course summary • Non-uniformity – formula lower bound (Andreev, Hastad) – monotone circuit lower bound (Razborov) Problem sets: – Barrington’s Theorem – formula lower bound for parity May 26, 2011 6 Course summary • Randomness – polynomial identity testing + Schwartz-Zippel – unique-SAT (Valiant-Vazirani Theorem) – Blum-Micali-Yao PRG – Nisan-Wigderson PRG – worst-case hardness ) average-case hardness – Trevisan extractor Problem sets: – Goldreich-Levin hard bit
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

lec18 - CS151 Complexity Theory Course Summary Lecture 18...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online