Yi Wu (CMU) Joint work with Parikshit Gopalan (MSR SVC) Ryan O’Donnell (CMU) David Zuckerman (UT...
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Yi Wu (CMU) Joint work with Parikshit Gopalan (MSR SVC) Ryan O’Donnell (CMU) David Zuckerman (UT Austin) Pseudorandom Generators for Halfspaces TexPoint
Yi Wu (CMU) Joint work with Parikshit Gopalan (MSR SVC) Ryan
ODonnell (CMU) David Zuckerman (UT Austin) Pseudorandom Generators
for Halfspaces TexPoint fonts used in EMF. Read the TexPoint manual
before you delete this box.: A AAAA
Slide 2
Outline Introduction Pseudorandom Generators Halfspaces
Pseudorandom Generators for Halfspaces Our Result Proof Conclusion
2
Slide 3
Deterministic Algorithm Program InputOutput The algorithm
deterministically outputs the correct result. 3
Slide 4
Randomized Algorithm Program Input Output Random Bits. The
algorithm outputs the correct result with high probability. 4
Slide 5
Randomized Algorithms Primality testing ST-connectivity Order
statistics Searching Polynomial and matrix identity verification
Interactive proof systems Faster algorithms for linear programming
Rounding linear program solutions to integer Minimum spanning trees
shortest paths minimum cuts Counting and enumeration Matrix
permanent Counting combinatorial structures Primality testing
ST-connectivity Order statistics Searching Polynomial and matrix
identity verification Interactive proof systems Faster algorithms
for linear programming Rounding linear program solutions to integer
Minimum spanning trees shortest paths minimum cuts Counting and
enumeration Matrix permanent Counting combinatorial structures
Primality testing ST-connectivity Order statistics Searching
Polynomial and matrix identity verification Interactive proof
systems Faster algorithms for linear programming Rounding linear
program solutions to integer Minimum spanning trees shortest paths
minimum cuts Counting and enumeration Matrix permanent Counting
combinatorial structures Primality testing ST-connectivity Order
statistics Searching Polynomial and matrix identity verification
Interactive proof systems Faster algorithms for linear programming
Rounding linear program solutions to integer Minimum spanning trees
shortest paths minimum cuts Counting and enumeration Matrix
permanent Counting combinatorial structures 5
Slide 6
Is Randomness Necessary? Open Problem: Can we simulate every
randomized polynomial time algorithm by a deterministic polynomial
time algorithm (the BPP P cojecture)? Derandomization of randomized
algorithms. Primality testing [AKS] ST-connectivity [Reingold]
Quadratic residues [?] 6
Slide 7
How to generate randomness? Question: How togenerate randomness
for every randomized algorithm? Simpler Question: How to generate
pseudorandomness for some class of programs? 7