CS6845 - Pseudorandomness

Meetings  

• Theme 1 : Derandomization Problem - Basics and Tools - 41 meetings

  • Meeting 01 : Mon, Feb 01, 08:00 am-08:50 am

  Administrative announcements. Informal introduction. Randomization as a tool. One-sided error vs Two-sided error versions. Examples - Frievalds algorithm.

  References	Lecture notes.
  Exercises
  Reading

  Administrative announcements. Informal introduction. Randomization as a tool. One-sided error vs Two-sided error versions. Examples - Frievalds algorithm.
  

  References

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  Lecture notes.

  • Meeting 02 : Tue, Feb 02, 12:00 pm-12:50 pm

  Freivald's algorithm. Formalization of Randomized Algorithm and Derandomization problem.

  References
  Exercises
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  Freivald's algorithm. Formalization of Randomized Algorithm and Derandomization problem.
  

  References

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  None

  • Meeting 03 : Thu, Feb 04, 11:00 am-11:50 am

  Trivial Derandomization by exhaustive enumeration. Model based derandomization. Pseudorandom generators. Fooling computations. Explicit construction problem.

  References
  Exercises
  Reading

  Trivial Derandomization by exhaustive enumeration. Model based derandomization. Pseudorandom generators. Fooling computations. Explicit construction problem.
  

  References

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  None

  • Meeting 04 : Fri, Feb 05, 10:00 am-10:50 am

  Randomness Extractors. Imperfect random sources. Role of seed. Closeness to uniform distribution. Explicit construction problem. Pseudorandom objects.

  References
  Exercises
  Reading

  Randomness Extractors. Imperfect random sources. Role of seed. Closeness to uniform distribution. Explicit construction problem. Pseudorandom objects.
  

  References

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  None

  • Meeting 05 : Mon, Feb 08, 08:00 am-08:50 am

  Polynomial Identity Testing. Blackbox and Whitebox. Univariate case. Amplification.

  References
  Exercises
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  Polynomial Identity Testing. Blackbox and Whitebox. Univariate case. Amplification.
  

  References

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  None

  • Meeting 06 : Tue, Feb 09, 12:00 pm-12:50 pm

  Multivariate PIT. Schwartz-Zippel Lemma.

  References
  Exercises
  Reading

  Multivariate PIT. Schwartz-Zippel Lemma.
  

  References

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  None

  • Meeting 07 : Thu, Feb 11, 11:00 am-11:50 am

  Analysis of the randomized algorithm for MaxCut. Quick review of random variables, expectation. Linearity of Expectation.

  References
  Exercises
  Reading

  Analysis of the randomized algorithm for MaxCut. Quick review of random variables, expectation. Linearity of Expectation.
  

  References

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  None

  • Meeting 08 : Fri, Feb 12, 10:00 am-10:50 am

  Method of conditional expectation. Deradnomization of MaxCut.

  References
  Exercises
  Reading

  Method of conditional expectation. Deradnomization of MaxCut.
  

  References

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  None

  • Meeting 09 : Mon, Feb 15, 08:00 am-08:50 am

  Back to the abstract set up. Making Algorithms Err less. Amplifying success probabilities. Case for one-sided vs two-sided error randomized algorithms.

  References
  Exercises
  Reading

  Back to the abstract set up. Making Algorithms Err less. Amplifying success probabilities. Case for one-sided vs two-sided error randomized algorithms.
  

  References

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  None

  • Meeting 10 : Tue, Feb 16, 12:00 pm-12:50 pm

  Sipser's Argument. Expander graphs. Properties Random walks(statements). Application to randomness efficient amplification of success probability (statement).

  References
  Exercises
  Reading

  Sipser's Argument. Expander graphs. Properties Random walks(statements). Application to randomness efficient amplification of success probability (statement).
  

  References

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  None

  • Meeting 11 : Thu, Feb 18, 11:00 am-11:50 am

  Amplification of one-sided error algorithms. Dispersers and application to amplification of one-sided error randomized algorithms.

  References
  Exercises
  Reading

  Amplification of one-sided error algorithms. Dispersers and application to amplification of one-sided error randomized algorithms.
  

  References

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  None

  • Meeting 12 : Fri, Feb 19, 10:00 am-10:50 am

  More tools from probability. Probabilistic Method. Hypergraph coloring.

  References
  Exercises
  Reading

  More tools from probability. Probabilistic Method. Hypergraph coloring.
  

  References

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  None

  • Meeting 13 : Thu, Mar 18, 11:00 am-11:50 am

  Expectation Method for showing the existence of objects.

  References
  Exercises
  Reading

  Expectation Method for showing the existence of objects.
  

  References

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  None

  • Meeting 14 : Fri, Mar 19, 10:00 am-10:50 am

  To Be Announced

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  To Be Announced
  

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  None

  • Meeting 15 : Mon, Mar 22, 08:00 am-08:50 am

  To Be Announced

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  To Be Announced
  

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  • Meeting 16 : Tue, Mar 23, 12:00 pm-12:50 pm

  To Be Announced

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  To Be Announced
  

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  • Meeting 17 : Thu, Mar 25, 11:00 am-11:50 am

  To Be Announced

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  To Be Announced
  

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  • Meeting 18 : Fri, Mar 26, 10:00 am-10:50 am

  To Be Announced

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  To Be Announced
  

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  • Meeting 19 : Mon, Mar 29, 08:00 am-08:50 am

  To Be Announced

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  • Meeting 20 : Tue, Mar 30, 12:00 pm-12:50 pm

  To Be Announced

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  • Meeting 21 : Thu, Apr 01, 11:00 am-11:50 am

  To Be Announced

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  • Meeting 22 : Fri, Apr 02, 10:00 am-10:50 am

  To Be Announced

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  • Meeting 23 : Mon, Apr 05, 08:00 am-08:50 am

  To Be Announced

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  • Meeting 24 : Tue, Apr 06, 12:00 pm-12:50 pm

  To Be Announced

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  • Meeting 25 : Thu, Apr 08, 11:00 am-11:50 am

  To Be Announced

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  • Meeting 26 : Fri, Apr 09, 10:00 am-10:50 am

  To Be Announced

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  • Meeting 27 : Mon, Apr 12, 08:00 am-08:50 am

  To Be Announced

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  • Meeting 28 : Tue, Apr 13, 12:00 pm-12:50 pm

  To Be Announced

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  • Meeting 29 : Thu, Apr 15, 11:00 am-11:50 am

  To Be Announced

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  • Meeting 30 : Fri, Apr 16, 10:00 am-10:50 am

  To Be Announced

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  • Meeting 31 : Mon, Apr 19, 08:00 am-08:50 am

  To Be Announced

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  • Meeting 32 : Tue, Apr 20, 12:00 pm-12:50 pm

  To Be Announced

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  • Meeting 33 : Thu, Apr 22, 11:00 am-11:50 am

  To Be Announced

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  • Meeting 34 : Fri, Apr 23, 10:00 am-10:50 am

  To Be Announced

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  • Meeting 35 : Mon, Apr 26, 08:00 am-08:50 am

  To Be Announced

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  To Be Announced
  

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  • Meeting 36 : Tue, Apr 27, 12:00 pm-12:50 pm

  To Be Announced

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  To Be Announced
  

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  • Meeting 37 : Thu, Apr 29, 11:00 am-11:50 am

  To Be Announced

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  • Meeting 38 : Fri, Apr 30, 10:00 am-10:50 am

  To Be Announced

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  • Meeting 39 : Mon, May 03, 08:00 am-08:50 am

  To Be Announced

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  To Be Announced
  

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  • Meeting 40 : Tue, May 04, 12:00 pm-12:50 pm

  To Be Announced

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  • Meeting 41 : Thu, May 06, 11:00 am-11:50 am

  To Be Announced

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  To Be Announced
  

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• Theme 2 : Pseudorandom Objects - 14 meetings

  • Meeting 42 : Mon, Feb 22, 08:00 am-08:50 am

  To Be Announced

  References
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  To Be Announced
  

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  • Meeting 43 : Tue, Feb 23, 12:00 pm-12:50 pm

  To Be Announced

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  To Be Announced
  

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  • Meeting 44 : Thu, Feb 25, 11:00 am-11:50 am

  To Be Announced

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  To Be Announced
  

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  • Meeting 45 : Fri, Feb 26, 10:00 am-10:50 am

  To Be Announced

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  To Be Announced
  

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  • Meeting 46 : Mon, Mar 01, 08:00 am-08:50 am

  To Be Announced

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  To Be Announced
  

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  • Meeting 47 : Tue, Mar 02, 12:00 pm-12:50 pm

  To Be Announced

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  To Be Announced
  

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  • Meeting 48 : Thu, Mar 04, 11:00 am-11:50 am

  To Be Announced

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  To Be Announced
  

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  • Meeting 49 : Fri, Mar 05, 10:00 am-10:50 am

  To Be Announced

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  • Meeting 50 : Mon, Mar 08, 08:00 am-08:50 am

  To Be Announced

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  • Meeting 51 : Tue, Mar 09, 12:00 pm-12:50 pm

  To Be Announced

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  • Meeting 52 : Thu, Mar 11, 11:00 am-11:50 am

  To Be Announced

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  • Meeting 53 : Fri, Mar 12, 10:00 am-10:50 am

  To Be Announced

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  To Be Announced
  

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  • Meeting 54 : Mon, Mar 15, 08:00 am-08:50 am

  To Be Announced

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  To Be Announced
  

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  • Meeting 55 : Tue, Mar 16, 12:00 pm-12:50 pm

  To Be Announced

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  To Be Announced
  

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