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CS151
Complexity Theory
Lecture 18
May 26, 2011
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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
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Course summary
•
Nondeterminism
–
NTIME hierarchy theorem
–
“NPintermediate” problems
(Ladner’s Theorem)
–
unary languages (likely) not NPcomplete
–
Savitch’s Theorem
–
ImmermanSzelepcsényi Theorem
Problem sets:
–
sparse
languages (likely) not NPcomplete
May 26, 2011
5
Course summary
•
Nonuniformity
–
formula lower bound (Andreev, Hastad)
–
monotone circuit lower bound (Razborov)
Problem sets:
–
Barrington’s Theorem
–
formula lower bound for parity
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Course summary
•
Randomness
–
polynomial identity testing + SchwartzZippel
–
uniqueSAT (ValiantVazirani Theorem)
–
BlumMicaliYao PRG
–
NisanWigderson PRG
–
worstcase hardness
)
averagecase hardness
–
Trevisan extractor
Problem sets:
–
GoldreichLevin hard bit
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This document was uploaded on 01/05/2012.
 Fall '09

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