CS6840 - Advanced Complexity Theory

Meetings  

• Theme 1 : Counting Complexity - 14 meetings

  • Meeting 01 : Tue, Jan 15, 12:00 pm-12:50 pm

  Administrative Announcements, Course Plan.

  References
  Exercises
  Reading

  Administrative Announcements, Course Plan.
  

  References

  :

  None

  • Meeting 02 : Thu, Jan 17, 11:00 am-11:50 am

  Counting vs Decision. #CYCLE is in P implies P = NP. Counting classess : FRP, #P, FPSPACE and inclusions and implications to decision world.

  References
  Exercises
  Reading

  Counting vs Decision. #CYCLE is in P implies P = NP. Counting classess : FRP, #P, FPSPACE and inclusions and implications to decision world.
  

  References

  :

  None

  • Meeting 03 : Fri, Jan 18, 10:00 am-10:50 am

  The bits and value of the #P function. Counting as a generalization of NP, BPP, RP, PP and Parity P. NP is contained in PP. inclusions.

  References
  Exercises
  Reading

  The bits and value of the #P function. Counting as a generalization of NP, BPP, RP, PP and Parity P. NP is contained in PP. inclusions.
  

  References

  :

  None

  • Meeting 04 : Mon, Jan 21, 08:00 am-08:50 am

  #P = FP if and only if PP = P. Harness among counting problems. The notion of hardness. Attempt 1 : parsimonious reductions.

  References
  Exercises
  Reading

  #P = FP if and only if PP = P. Harness among counting problems. The notion of hardness. Attempt 1 : parsimonious reductions.
  

  References

  :

  None

  • Meeting 05 : Tue, Jan 22, 12:00 pm-12:50 pm

  #P-hardness definition. #SAT is #P-complete. #IND-SET is #P-complete. Shortcomings of the theory. General oracle query model of #P-completeness.

  References
  Exercises
  Reading

  #P-hardness definition. #SAT is #P-complete. #IND-SET is #P-complete. Shortcomings of the theory. General oracle query model of #P-completeness.
  

  References

  :

  None

  • Meeting 06 : Thu, Jan 24, 11:00 am-11:50 am

  The permanent and the determinant functions. Combinatorial interpretation of permanent of matrix with 0-1 entries. Counting perfect matchings.

  References
  Exercises
  Reading

  The permanent and the determinant functions. Combinatorial interpretation of permanent of matrix with 0-1 entries. Counting perfect matchings.
  

  References

  :

  None

  • Meeting 07 : Fri, Jan 25, 10:00 am-10:50 am

  Permanent if integer matrices. Combinatorial interpretation in terms of cycle covers. The upper bound of FP^#P. Permanent over {-1,0,1} matrices is #P-complete. Proof idea, Gadget construction.

  References
  Exercises
  Reading

  Permanent if integer matrices. Combinatorial interpretation in terms of cycle covers. The upper bound of FP^#P. Permanent over {-1,0,1} matrices is #P-complete. Proof idea, Gadget construction.
  

  References

  :

  None

  • Meeting 08 : Tue, Jan 29, 12:00 pm-12:50 pm

  Details of #P-completeness reduction. Reduction from PERM(-1,0,1) to PERM(0,1,...,n), and then to PERM(0,1).

  References	<a href="http://pages.cs.wisc.edu/~holger/papers/DHMTW12final.pdf">Page 10-11 of this paper</a>.
  Exercises
  Reading	Counting complexity chapter in the Arora-Barak Textbook. The gadget is slightly more complicated than what we did in class - but that was the first one discovered by Valiant in 1979.

  Details of #P-completeness reduction. Reduction from PERM(-1,0,1) to PERM(0,1,...,n), and then to PERM(0,1).
  

  References	:	Page 10-11 of this paper.
  Reading	:	Counting complexity chapter in the Arora-Barak Textbook. The gadget is slightly more complicated than what we did in class - but that was the first one discovered by Valiant in 1979.

  • Meeting 09 : Thu, Jan 31, 11:00 am-11:50 am

  Toda's Theorem. The basic steps. U-SAT : Valiant Vazirani Reduction.

  References
  Exercises
  Reading

  Toda's Theorem. The basic steps. U-SAT : Valiant Vazirani Reduction.
  

  References

  :

  None

  • Meeting 10 : Sun, Feb 03, 02:00 pm-03:00 pm

  Hash families, Pairwise independent hashing. Proof of the uniqueness lemma. Reduction to Parity SAT. Amplification of success probability. Generalizations to show that PH BP-reduces to Parity-SAT.

  References
  Exercises
  Reading

  Hash families, Pairwise independent hashing. Proof of the uniqueness lemma. Reduction to Parity SAT. Amplification of success probability. Generalizations to show that PH BP-reduces to Parity-SAT.
  

  References

  :

  None

  • Meeting 11 : Sun, Feb 03, 03:00 pm-04:00 pm

  Any language that BP-reduces to Parity-SAT can be decided with a counting oracle. Proof idea. Toda's polynomials. Details of the proof.

  References
  Exercises
  Reading

  Any language that BP-reduces to Parity-SAT can be decided with a counting oracle. Proof idea. Toda's polynomials. Details of the proof.
  

  References

  :

  None

  • Meeting 12 : Mon, Feb 04, 08:00 am-08:50 am

  Success Probability Amplification. Derandomization Problem. NP vs BPP.

  References
  Exercises
  Reading

  Success Probability Amplification. Derandomization Problem. NP vs BPP.
  

  References

  :

  None

  • Meeting 13 : Tue, Feb 05, 12:00 pm-12:50 pm

  Two consequences of amplification lemma BPP is in Sigma^2. BPP is in P/poly.

  References
  Exercises
  Reading

  Two consequences of amplification lemma BPP is in Sigma^2. BPP is in P/poly.
  

  References

  :

  None

  • Meeting 14 : Thu, Feb 07, 11:00 am-11:50 am

  The class P/poly. Meyer's theorem (statement). Karp-Lipton Collapse theorem : If NP is contained in P/poly then PH Collapses.

  References
  Exercises
  Reading

  The class P/poly. Meyer's theorem (statement). Karp-Lipton Collapse theorem : If NP is contained in P/poly then PH Collapses.
  

  References

  :

  None

• Theme 2 : Probablistic Proof Systems - 19 meetings

  • Meeting 15 : Fri, Feb 08, 10:00 am-10:50 am

  Interactive Proof Systems. Deterministic, Randomized. Protocol for GI-bar. Public vs Private randomness.

  References
  Exercises
  Reading

  Interactive Proof Systems. Deterministic, Randomized. Protocol for GI-bar. Public vs Private randomness.
  

  References

  :

  None

  • Meeting 16 : Mon, Feb 11, 08:00 am-08:50 am

  Interactive Proofs for the permanent, LFKN protocol.

  References
  Exercises
  Reading

  Interactive Proofs for the permanent, LFKN protocol.
  

  References

  :

  None

  • Meeting 17 : Tue, Feb 12, 12:00 pm-12:50 pm

  Arithmetization, LFKN protocol on the sum-expression.

  References
  Exercises
  Reading

  Arithmetization, LFKN protocol on the sum-expression.
  

  References

  :

  None

  • Meeting 18 : Thu, Feb 14, 11:00 am-11:50 am

  Lecture cancelled. Compensatory lecture TBA.

  References
  Exercises
  Reading

  Lecture cancelled. Compensatory lecture TBA.
  

  References

  :

  None

  • Meeting 19 : Fri, Feb 15, 10:00 am-10:50 am

  Shamir's degree reduction method. IP=PSPACE. PSPACE algorithm for IP.

  References
  Exercises
  Reading

  Shamir's degree reduction method. IP=PSPACE. PSPACE algorithm for IP.
  

  References

  :

  None

  • Meeting 20 : Sat, Feb 16, 02:00 pm-03:00 pm

  Public Coin Protocols. The class AM. Protocol for GI-bar. Goldwaser-Sipser Set Lower Bound Protocol.

  References
  Exercises
  Reading

  Public Coin Protocols. The class AM. Protocol for GI-bar. Goldwaser-Sipser Set Lower Bound Protocol.
  

  References

  :

  None

  • Meeting 21 : Sat, Feb 16, 03:00 pm-04:00 pm

  Perfect completeness for protocols. If GI is NP-complete then PH is in Sigma^2.

  References
  Exercises
  Reading

  Perfect completeness for protocols. If GI is NP-complete then PH is in Sigma^2.
  

  References

  :

  None

  • Meeting 22 : Mon, Feb 18, 08:00 am-08:50 am

  Achieving perfect completeness for Arthur-Merlin Games.

  References
  Exercises
  Reading

  Achieving perfect completeness for Arthur-Merlin Games.
  

  References

  :

  None

  • Meeting 23 : Wed, Feb 20, 04:15 pm-05:30 pm

  MA is contained in AM. <br> Set-Lower Bound is very general : From private coin protocol to public coin protocols. <br> Probabilistically Checkable Proofs, Basic definitions. GAP3SAT problem.

  References
  Exercises
  Reading

  MA is contained in AM.
  Set-Lower Bound is very general : From private coin protocol to public coin protocols.
  Probabilistically Checkable Proofs, Basic definitions. GAP3SAT problem.
  

  References

  :

  None

  • Meeting 24 : Thu, Feb 21, 11:00 am-11:50 am

  qCSP, L is in PCP(O(log n), q) if and only if L reduces to qCSP. Reduction from qCSP to GAPSAT.

  References
  Exercises
  Reading

  qCSP, L is in PCP(O(log n), q) if and only if L reduces to qCSP. Reduction from qCSP to GAPSAT.
  

  References

  :

  None

  • Meeting 25 : Fri, Feb 22, 10:00 am-10:50 am

  Inapproximability of Independent set Problem. GAPCSP to GAPIS. PCP for LIN, Attempts

  References
  Exercises
  Reading

  Inapproximability of Independent set Problem. GAPCSP to GAPIS. PCP for LIN, Attempts
  

  References

  :

  None

  • Meeting 26 : Sat, Feb 23, 10:00 am-11:00 am

  Proof in the long-code form. Need of linearity testing. Linearity testing. Local decoding. The proof of PCP for LIN.

  References
  Exercises
  Reading

  Proof in the long-code form. Need of linearity testing. Linearity testing. Local decoding. The proof of PCP for LIN.
  

  References

  :

  None

  • Meeting 27 : Mon, Mar 11, 08:00 am-08:50 am

  Proof of Linearity testing.

  References
  Exercises
  Reading

  Proof of Linearity testing.
  

  References

  :

  None

  • Meeting 28 : Tue, Mar 12, 12:00 pm-12:50 pm

  Generalization to Quadratic Programs.

  References
  Exercises
  Reading

  Generalization to Quadratic Programs.
  

  References

  :

  None

  • Meeting 29 : Thu, Mar 14, 11:00 am-11:50 am

  Dinur's Proof of PCP theorem. The proof outline. Query reduction step.

  References
  Exercises
  Reading

  Dinur's Proof of PCP theorem. The proof outline. Query reduction step.
  

  References

  :

  None

  • Meeting 30 : Fri, Mar 15, 10:00 am-10:50 am

  Degree reduction.

  References
  Exercises
  Reading

  Degree reduction.
  

  References

  :

  None

  • Meeting 31 : Sat, Mar 16, 11:00 am-11:50 am

  Expanderization.

  References
  Exercises
  Reading

  Expanderization.
  

  References

  :

  None

  • Meeting 32 : Sat, Mar 16, 12:00 pm-12:50 pm

  Gap Amplification (construction)

  References
  Exercises
  Reading

  Gap Amplification (construction)
  

  References

  :

  None

  • Meeting 33 : Mon, Mar 18, 08:00 am-08:50 am

  Gap Amplification (argument). Alphabet reduction.

  References
  Exercises
  Reading

  Gap Amplification (argument). Alphabet reduction.
  

  References

  :

  None

• Theme 3 : Circuit Complexity and Lower Bounds - 24 meetings

  • Meeting 34 : Tue, Mar 19, 12:00 pm-12:50 pm

  Boolean Circuit Model of Computation. The first few questions. Why circuits? Connections to parallel algorithm design. The relevant parameters of the circuit model - Size, depth, fanin. <br> What is allowed as a gate? Basis and completeness. Post's characterization of a complete basis (statement).

  References	Class notes.
  Exercises
  Reading

  Boolean Circuit Model of Computation. The first few questions. Why circuits? Connections to parallel algorithm design. The relevant parameters of the circuit model - Size, depth, fanin.
  What is allowed as a gate? Basis and completeness. Post's characterization of a complete basis (statement).
  

  References

  :

  Class notes.

  • Meeting 35 : Thu, Mar 21, 11:00 am-11:50 am

  P/poly = functions computed by polynomial sized circuits. The circuit lower-bound problem. Uniformity, Log-space Uniformity. P is computed by uniform polysize circuits. Review of parameters and questions.

  References
  Exercises
  Reading

  P/poly = functions computed by polynomial sized circuits. The circuit lower-bound problem. Uniformity, Log-space Uniformity. P is computed by uniform polysize circuits. Review of parameters and questions.
  

  References

  :

  None

  • Meeting 36 : Fri, Mar 22, 10:00 am-10:50 am

  Shannon's counting argument. Lupanov's construction.

  References
  Exercises
  Reading

  Shannon's counting argument. Lupanov's construction.
  

  References

  :

  None

  • Meeting 37 : Sat, Mar 23, 04:30 pm-05:30 pm

  Gate Elimination Argument for Circuit Lower Bounds. Lower bounds for Parity and Threshold.

  References
  Exercises
  Reading

  Gate Elimination Argument for Circuit Lower Bounds. Lower bounds for Parity and Threshold.
  

  References

  :

  None

  • Meeting 38 : Sat, Mar 23, 05:30 pm-06:30 pm

  Simple functions and their circuits, PARITY, ADD.

  References
  Exercises
  Reading

  Simple functions and their circuits, PARITY, ADD.
  

  References

  :

  None

  • Meeting 39 : Mon, Mar 25, 08:00 am-08:50 am

  The class NC.The class AC-hierarchy. Interleaving with NC hierarchy. Uniform NC^1 is contained in L.

  References
  Exercises
  Reading

  The class NC.The class AC-hierarchy. Interleaving with NC hierarchy. Uniform NC^1 is contained in L.
  

  References

  :

  None

  • Meeting 40 : Tue, Mar 26, 10:00 am-10:50 am

  NL is contained in uniform-AC^1. Back to NC^1, Adding n, n-bit numbers. Trivial AC^1 upper bound. Offman's technique and the NC^1 upper bound. Majority in NC^1. Constant depth reductions.

  References
  Exercises
  Reading

  NL is contained in uniform-AC^1. Back to NC^1, Adding n, n-bit numbers. Trivial AC^1 upper bound. Offman's technique and the NC^1 upper bound. Majority in NC^1. Constant depth reductions.
  

  References

  :

  None

  • Meeting 41 : Thu, Mar 28, 11:00 am-11:50 am

  Zooming in to NC^1. Review of constant depth reductions. <br>Six Problems : ADD(n,n). MULT(2,n), Th(n,k), BCOUNT, MAJ. <br>NC^1 upper bounds. Constant depth reductions among these problems. Motivation and definition of the class TC^0.

  References
  Exercises
  Reading

  Zooming in to NC^1. Review of constant depth reductions.
  Six Problems : ADD(n,n). MULT(2,n), Th(n,k), BCOUNT, MAJ.
  NC^1 upper bounds. Constant depth reductions among these problems. Motivation and definition of the class TC^0.
  

  References

  :

  None

  • Meeting 42 : Mon, Apr 01, 08:15 am-08:50 am

  Symmetric Functions are in TC^0. Motivation and definition of the class ACC^0. The hierarchy interleaving with NC and AC hierarchies.

  References
  Exercises
  Reading

  Symmetric Functions are in TC^0. Motivation and definition of the class ACC^0. The hierarchy interleaving with NC and AC hierarchies.
  

  References

  :

  None

  • Meeting 43 : Tue, Apr 02, 12:00 pm-12:50 pm

  Formulas, BF = NC^1. Formula size lower bounds,

  References
  Exercises
  Reading

  Formulas, BF = NC^1. Formula size lower bounds,
  

  References

  :

  None

  • Meeting 44 : Thu, Apr 04, 11:00 am-11:50 am

  Sabbotavskaya's Lower bound using Restrictions. Lower Bounds for Parity.

  References
  Exercises
  Reading

  Sabbotavskaya's Lower bound using Restrictions. Lower Bounds for Parity.
  

  References

  :

  None

  • Meeting 45 : Fri, Apr 05, 10:00 am-10:50 am

  Nechiporuk's Method. Lower bound for Indirect Access function.

  References
  Exercises
  Reading

  Nechiporuk's Method. Lower bound for Indirect Access function.
  

  References

  :

  None

  • Meeting 46 : Sat, Apr 06, 08:15 am-09:15 am

  Proof of Nechiporuk's Theorem.

  References
  Exercises
  Reading

  Proof of Nechiporuk's Theorem.
  

  References

  :

  None

  • Meeting 47 : Sat, Apr 06, 09:15 am-10:15 am

  Nechiporuk's "hardness embedding" technique. Extensions of Sabotavskaya's argument to random restrictions. Andreev's Lower Bound. Shrinkage Exponent.

  References
  Exercises
  Reading

  Nechiporuk's "hardness embedding" technique. Extensions of Sabotavskaya's argument to random restrictions. Andreev's Lower Bound. Shrinkage Exponent.
  

  References

  :

  None

  • Meeting 48 : Mon, Apr 08, 12:00 pm-12:50 pm

  Constant depth circuits cannot compute parity in polysize. Overview of the proof. Trivial cases like AND, OR. First nontrivial case - DNF. The switching Lemma. Proof of Switching Lemma.

  References	<a href="homes.cs.washington.edu/~beame/papers/primer.ps">Switching Lemma Primer</a>.
  Exercises
  Reading

  Constant depth circuits cannot compute parity in polysize. Overview of the proof. Trivial cases like AND, OR. First nontrivial case - DNF. The switching Lemma. Proof of Switching Lemma.
  

  References

  :

  Switching Lemma Primer.

  • Meeting 49 : Tue, Apr 09, 12:00 pm-12:50 pm

  Inductive Argument. Exponential size lower bounds for constant depth circuits computing parity.

  References	<a href="homes.cs.washington.edu/~beame/papers/primer.ps">Switching Lemma Primer</a>.
  Exercises
  Reading

  Inductive Argument. Exponential size lower bounds for constant depth circuits computing parity.
  

  References

  :

  Switching Lemma Primer.

  • Meeting 50 : Fri, Apr 12, 10:00 am-10:50 am

  Representation of Boolean functions by polynomials. Upper bound on the degree required to agree with a size s depth d ckt on most of the inputs.

  References	<a href="http://users-cs.au.dk/arnsfelt/CT08/scribenotes/lecture10.pdf">Notes - Kristoffer Hansen</a>
  Exercises
  Reading

  Representation of Boolean functions by polynomials. Upper bound on the degree required to agree with a size s depth d ckt on most of the inputs.
  

  References

  :

  Notes - Kristoffer Hansen

  • Meeting 51 : Mon, Apr 15, 08:00 am-08:50 am

  If we can represent PARITY using a polynomial of degree t, then we can represent all functions with polynomials of degree (n+t)/2. But there are not that many polynomials whose degree is that small but there are too many Boolean functions. Razborov-Smolensky lower bound for PARITY.

  References	<a href="http://users-cs.au.dk/arnsfelt/CT08/scribenotes/lecture10.pdf">Notes - Kristoffer Hansen</a>
  Exercises
  Reading

  If we can represent PARITY using a polynomial of degree t, then we can represent all functions with polynomials of degree (n+t)/2. But there are not that many polynomials whose degree is that small but there are too many Boolean functions. Razborov-Smolensky lower bound for PARITY.
  

  References

  :

  Notes - Kristoffer Hansen

  • Meeting 52 : Tue, Apr 16, 12:00 pm-12:50 pm

  Monotone Circuits, Lower Bounds known. Negation Limited circuits - the story so far. Razoborov's lower bound for monotone circuits. Proof strategy.

  References	<a href="www.cmi.ac.in/~ramprasad/lecturenotes/raz_clique.pdf">Ramprasad's lecture notes based on Arvind's lecture</a>.
  Exercises
  Reading

  Monotone Circuits, Lower Bounds known. Negation Limited circuits - the story so far. Razoborov's lower bound for monotone circuits. Proof strategy.
  

  References

  :

  Ramprasad's lecture notes based on Arvind's lecture.

  • Meeting 53 : Thu, Apr 18, 11:00 am-11:50 am

  Clique Approximators. Construction of the approximate circuit. Sunflower Lemma.

  References	<a href="www.cmi.ac.in/~ramprasad/lecturenotes/raz_clique.pdf">Ramprasad's lecture notes based on Arvind's lecture</a>.
  Exercises
  Reading

  Clique Approximators. Construction of the approximate circuit. Sunflower Lemma.
  

  References

  :

  Ramprasad's lecture notes based on Arvind's lecture.

  • Meeting 54 : Fri, Apr 19, 10:00 am-10:50 am

  Lower bound on the error estimate for the approximate circuit. Upper bound on the error by counting that for each gate. The lower bound argument.

  References	<a href="www.cmi.ac.in/~ramprasad/lecturenotes/raz_clique.pdf">Ramprasad's lecture notes based on Arvind's lecture</a>.
  Exercises
  Reading

  Lower bound on the error estimate for the approximate circuit. Upper bound on the error by counting that for each gate. The lower bound argument.
  

  References

  :

  Ramprasad's lecture notes based on Arvind's lecture.

  • Meeting 55 : Mon, Apr 22, 08:00 am-08:50 am

  Branching Programs and Skew circuits. From space bounded algorithms to Branching Programs. Width of the Branching Programs.

  References	<a href="http://www.ccs.neu.edu/home/viola/classes/gems-08/lectures/le11.pdf"></a>
  Exercises
  Reading

  Branching Programs and Skew circuits. From space bounded algorithms to Branching Programs. Width of the Branching Programs.
  

  References

  :

  • Meeting 56 : Tue, Apr 23, 12:00 pm-12:50 pm

  Programs over groups. Permutations. Conjugates, Cycle conjugacy lemma.

  References	<a href="http://www.ccs.neu.edu/home/viola/classes/gems-08/lectures/le11.pdf"></a>
  Exercises
  Reading

  Programs over groups. Permutations. Conjugates, Cycle conjugacy lemma.
  

  References

  :

  • Meeting 57 : Wed, Apr 24, 05:30 pm-06:30 pm

  Barrington's theorem for width-5. Role of Non-solvability of the group.

  References	<a href="http://www.ccs.neu.edu/home/viola/classes/gems-08/lectures/le11.pdf"></a>
  Exercises
  Reading

  Barrington's theorem for width-5. Role of Non-solvability of the group.
  

  References

  :

• Theme 4 : Hardness vs Randomness - 4 meetings

  • Meeting 58 : Fri, Apr 26, 10:00 am-10:50 am

  Derandomization Problem, Hardness assumptions. Pseudo random generators.

  References	<a href="http://www-cc.cs.uni-saarland.de/media/oldmaterial/derandcircuit.pdf">Derandomization and Circuit Lower Bounds</a> Notes by Markus Blaeser</a>
  Exercises
  Reading

  Derandomization Problem, Hardness assumptions. Pseudo random generators.
  

  References

  :

  Derandomization and Circuit Lower Bounds Notes by Markus Blaeser

  • Meeting 59 : Fri, Apr 26, 05:00 pm-06:30 am

  Nisan-Wigderson generator, NW Design. Proof of pseudorandomness. Intuition for hybrid argument.

  References	<a href="http://www-cc.cs.uni-saarland.de/media/oldmaterial/derandcircuit.pdf">Derandomization and Circuit Lower Bounds</a> Notes by Markus Blaeser</a>
  Exercises
  Reading

  Nisan-Wigderson generator, NW Design. Proof of pseudorandomness. Intuition for hybrid argument.
  

  References

  :

  Derandomization and Circuit Lower Bounds Notes by Markus Blaeser

  • Meeting 60 : Mon, Apr 29, 08:00 am-08:50 am

  Details of Hybrid Argument.

  References	<a href="http://www-cc.cs.uni-saarland.de/media/oldmaterial/derandcircuit.pdf">Derandomization and Circuit Lower Bounds</a> Notes by Markus Blaeser</a>
  Exercises
  Reading

  Details of Hybrid Argument.
  

  References

  :

  Derandomization and Circuit Lower Bounds Notes by Markus Blaeser

  • Meeting 61 : Mon, Apr 29, 05:00 pm-06:30 pm

  Crash course on coding theory, Local Decoding, Local list decoding. Using codes to reduce from Worst case hard functions to Average Case hard function. <br> From Derandomization to Hard Functions - Impagliazzo-Kabanets Theorem.

  References	<ul> <li><a href="http://www-cc.cs.uni-saarland.de/media/oldmaterial/derandcircuit.pdf">Derandomization and Circuit Lower Bounds</a> Notes by Markus Blaeser</a></li> <li>[AB] Textbook section 20.4, assumed Lemma 20.20.</li> </ul>
  Exercises
  Reading

  Crash course on coding theory, Local Decoding, Local list decoding. Using codes to reduce from Worst case hard functions to Average Case hard function.
  From Derandomization to Hard Functions - Impagliazzo-Kabanets Theorem.
  

  References

  :

  Derandomization and Circuit Lower Bounds Notes by Markus Blaeser [AB] Textbook section 20.4, assumed Lemma 20.20.

• Evaluation Meetings - 18 meetings

  • Meeting 62 : Mon, Apr 15, 04:30 pm-05:30 pm

  Interim Meeting <br> 16:30 - 17:00 : Sidhartha Sivakumar : <br> 17:00 - 17:30 : Karthik Abhinav

  References
  Exercises
  Reading

  Interim Meeting
  16:30 - 17:00 : Sidhartha Sivakumar :
  17:00 - 17:30 : Karthik Abhinav
  

  References

  :

  None

  • Meeting 63 : Wed, Apr 17, 04:00 pm-06:00 pm

  Interim Meeting <br> 16:00 - 16:30 : Saikrishna Badrinarayanan <br> 16:30 - 17:00 : Gaurav Singh <br>

  References
  Exercises
  Reading

  Interim Meeting
  16:00 - 16:30 : Saikrishna Badrinarayanan
  16:30 - 17:00 : Gaurav Singh
  
  

  References

  :

  None

  • Meeting 64 : Thu, Apr 18, 04:30 pm-05:30 pm

  Interim Meeting <br> 16:30 - 17:00 : Anant Dhayal <br> 17:00 - 17:30 : Ramnath Jayachandran<br> 17:30 - 18:00 : Vishal Pandya

  References
  Exercises
  Reading

  Interim Meeting
  16:30 - 17:00 : Anant Dhayal
  17:00 - 17:30 : Ramnath Jayachandran
  17:30 - 18:00 : Vishal Pandya
  

  References

  :

  None

  • Meeting 65 : Fri, Apr 19, 11:00 am-12:00 pm

  Interim Meeting: <br> 11:00 - 11:30 : Akshay Degwekar<br> 11:30 - 12:00 : Alexandra Weber & Niels Ströher.

  References
  Exercises
  Reading

  Interim Meeting:
  11:00 - 11:30 : Akshay Degwekar
  11:30 - 12:00 : Alexandra Weber & Niels Ströher.
  

  References

  :

  None

  • Meeting 66 : Wed, Apr 24, 09:00 am-10:00 am

  Karthik Abhinav: <a href="http://www.cs.sfu.ca/~kabanets/Research/isolation.html">Is Valiant-Vazirani Lemma Probability improvable?</a>.

  References
  Exercises
  Reading

  Karthik Abhinav: Is Valiant-Vazirani Lemma Probability improvable?.
  

  References

  :

  None

  • Meeting 67 : Wed, Apr 24, 10:00 am-11:00 am

  Vishal Pandya: <a href="http://people.csail.mit.edu/dmoshkov/courses/adv-comp/accnexp.pdf">Lower Bounds from satisfiability testing algorithms</a>.

  References
  Exercises
  Reading

  Vishal Pandya: Lower Bounds from satisfiability testing algorithms.
  

  References

  :

  None

  • Meeting 68 : Wed, Apr 24, 11:00 am-12:00 pm

  Sidhartha Sivakumar: <a href="">Characterization of Complete Basis.</a> <br> (reference will be sent separately).

  References
  Exercises
  Reading

  Sidhartha Sivakumar: Characterization of Complete Basis.
  (reference will be sent separately).
  

  References

  :

  None

  • Meeting 69 : Wed, Apr 24, 12:00 pm-01:00 pm

  Saikrishna Badrinarayanan: <a href="http://www.cse.iitk.ac.in/users/abhik/files/ss.pdf">Two Applications of Inductive Counting</a>.

  References
  Exercises
  Reading

  Saikrishna Badrinarayanan: Two Applications of Inductive Counting.
  

  References

  :

  None

  • Meeting 70 : Thu, Apr 25, 12:00 pm-12:30 pm

  Interim Meeting : <br> 12:30 - 13:00 : Saurabh Verma.

  References
  Exercises
  Reading

  Interim Meeting :
  12:30 - 13:00 : Saurabh Verma.
  

  References

  :

  None

  • Meeting 71 : Sat, Apr 27, 09:00 am-10:00 am

  Anant Dhayal: <a href="http://www.cs.utexas.edu/~klivans/r6.ps">Linear Advice for Randomized Logarithmic Space</a>.

  References
  Exercises
  Reading

  Anant Dhayal: Linear Advice for Randomized Logarithmic Space.
  

  References

  :

  None

  • Meeting 72 : Sat, Apr 27, 10:00 am-11:00 am

  Ramnath Jayachandran: <a href="http://eccc.hpi-web.de/report/2012/059/download/">Uniform Circuits, Lower Bounds, and QBF Algorithms</a>.

  References
  Exercises
  Reading

  Ramnath Jayachandran: Uniform Circuits, Lower Bounds, and QBF Algorithms.
  

  References

  :

  None

  • Meeting 73 : Sat, Apr 27, 11:00 am-12:00 pm

  Saurabh Verma: <a href="http://people.csail.mit.edu/madhu/ST05/scribe/lect04.ps">BenOr-Cleve Construction of Constant-width Branching Programs.</a>

  References
  Exercises
  Reading

  Saurabh Verma: BenOr-Cleve Construction of Constant-width Branching Programs.
  

  References

  :

  None

  • Meeting 74 : Sat, Apr 27, 12:00 pm-01:00 pm

  Gaurav Singh: <a href="">Polylogarithmic Threshold is in AC^0.</a><br> (reference will be sent).

  References
  Exercises
  Reading

  Gaurav Singh: Polylogarithmic Threshold is in AC^0.
  (reference will be sent).
  

  References

  :

  None

  • Meeting 75 : Mon, Apr 29, 02:00 pm-03:00 pm

  Akshay Degwekar: <a href="www.wisdom.weizmann.ac.il/~ranraz/publications/Ptensor.pdf">Tensor Ranks and Arithmetic Formula Lower Bounds</a>.

  References
  Exercises
  Reading

  Akshay Degwekar: Tensor Ranks and Arithmetic Formula Lower Bounds.
  

  References

  :

  None

  • Meeting 76 : Mon, Apr 29, 03:00 pm-04:00 pm

  Neils & Alexandra : <a href="http://ftp.cs.rutgers.edu/pub/allender/amplifying.pdf">Amplifying Lower Bounds by Means of Self-Reducibility.</a>

  References
  Exercises
  Reading

  Neils & Alexandra : Amplifying Lower Bounds by Means of Self-Reducibility.
  

  References

  :

  None

  • Meeting 77 : Mon, Apr 29, 04:00 pm-05:00 pm

  Niels & Alexandra: <a href="http://ftp.cs.rutgers.edu/pub/allender/pathetic2.pdf">Uniform Derandomization from Pathetic Lower Bounds.</a>

  References
  Exercises
  Reading

  Niels & Alexandra: Uniform Derandomization from Pathetic Lower Bounds.
  

  References

  :

  None

  • Meeting 78 : Wed, May 01, 11:00 am-06:00 pm

  Viva : Schedule (30 minutes each)<br> <ul> <li>11:00 - 11:30 : Akshay Degewekar </li> <li>11:35 - 12:05 : Saikrishna Badarinarayanan</li> <li>12:10 - 12:40 : Karthik Abhinav</li> <li>12:45 - 13:15 : Sidhartha S.</li> <li>14:00 - 14:30 : Niels Stroeher</li> <li>14:35 - 15:05 : Alexandra Weber</li> <li>15:10 - 15:40 : Gaurav Singh</li> <li>15:45 - 16:15 : Saurabh Kumar Verma</li> <li>16:20 - 16:50 : Vishal Pandya</li> <li>16:55 - 17:25 : Ramnath Jayachandran</li> <li>17:30 - 18:00 : Anant Dhayal</li> </ul>

  References
  Exercises
  Reading

  Viva : Schedule (30 minutes each)
  

  • 11:00 - 11:30 : Akshay Degewekar
  • 11:35 - 12:05 : Saikrishna Badarinarayanan
  • 12:10 - 12:40 : Karthik Abhinav
  • 12:45 - 13:15 : Sidhartha S.
  • 14:00 - 14:30 : Niels Stroeher
  • 14:35 - 15:05 : Alexandra Weber
  • 15:10 - 15:40 : Gaurav Singh
  • 15:45 - 16:15 : Saurabh Kumar Verma
  • 16:20 - 16:50 : Vishal Pandya
  • 16:55 - 17:25 : Ramnath Jayachandran
  • 17:30 - 18:00 : Anant Dhayal

  
  

  References

  :

  None

  • Meeting 79 : Wed, May 01, 09:00 am-10:30 am

  Endsem Exam

  References
  Exercises
  Reading

  Endsem Exam
  

  References

  :

  None