- Meeting 18 : Tue, Feb 15, 12:00 pm-12:50 pm
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Circuit complexty. The model and resources. Connection to parallel computation and algorithms. Trivial circuit for any function. Size, depth, fanin.
- Meeting 19 : Thu, Feb 17, 11:00 am-11:50 am
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P/poly is exactly the class of languages that are computed by polynomial-size circuits. Uniformity in circuits. P is equal to P-uniform-PSIZE.
- Meeting 20 : Fri, Feb 18, 10:00 am-10:50 am
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Circuit lower bound problem. Shannon's lower bound. Lupanov's matching upper bound.
- Meeting 21 : Mon, Feb 21, 08:00 am-08:50 am
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Exercises | |
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Restricted circuits characterize complexity classes too. Skew circuits and NL.
- Meeting 22 : Tue, Feb 22, 12:00 pm-12:50 pm
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Gate-Elimnation Argument. Example circuits. Adder circuit. Carry-look-ahead constant depth poly size adder.
- Meeting 23 : Thu, Feb 24, 11:00 am-11:50 am
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More circuit upper bounds. Adding n n-bit numbers. Offman's trick. Multiplying two n-bit numbers. The class NC^1. AC^0. The hierarchy.
- Meeting 24 : Fri, Feb 25, 10:00 am-10:50 am
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Exercises | |
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More circuit upper bounds. Cool tricks. Adding log n n-bit numbers in AC^0. Constant depth reductions.
- Meeting 25 : Mon, Feb 28, 08:00 am-08:50 am
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Exercises | |
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More constant depth reductions. The class TC^0 and ACC^0.
- Meeting 26 : Tue, Mar 01, 12:00 pm-12:50 pm
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Exercises | |
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NC^1 is contained in L and NL is contained in AC^1 (in fact, in SAC^1).
- Meeting 27 : Thu, Mar 03, 11:00 am-11:50 am
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Exercises | |
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Restricted circuits again. Polysize Boolean formulas can be computed by circuits of log depth with polysize. Spira's depth reduction. BF = NC^1
- Meeting 28 : Fri, Mar 04, 10:00 am-10:50 am
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Formula size lower bounds. Khrapchenko's measure-based lower bound.
- Meeting 29 : Mon, Mar 07, 08:00 am-08:50 am
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Exercises | |
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Nechiporuk's Formula lower bound.
- Meeting 30 : Tue, Mar 08, 12:00 pm-12:50 pm
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Exercises | |
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Sabbotvskaya's Formula lower bound. Random restrictions.
- Meeting 31 : Thu, Mar 10, 11:00 am-11:50 am
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Random restrictions and shrinkage exponent. Formula lower bound.
- Meeting 32 : Fri, Mar 11, 10:00 am-10:50 am
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Andreev's Cubic Formula-size Lower bound.
- Meeting 33 : Mon, Mar 14, 08:00 am-08:50 am
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PARITY is not in AC^0. The intuitive buildup of the proof and basic setup. Canonical decision trees. The statement of the switching Lemma. Overview assuming switching lemma.
- Meeting 34 : Tue, Mar 15, 12:00 pm-12:50 pm
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Lower bounds for parity assuming the switching lemma. The inductive building of the restrictions.
- Meeting 35 : Thu, Mar 17, 11:00 am-11:50 am
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Razborov's proof of the switching Lemma. The injection from the bad restrictions.
- Meeting 36 : Fri, Mar 18, 10:00 am-10:50 am
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"Holi"day !! - no class.
- Meeting 37 : Mon, Mar 21, 08:00 am-08:50 am
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To Be Announced
- Meeting 38 : Tue, Mar 22, 12:00 pm-12:50 pm
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Exercises | |
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To Be Announced
- Meeting 39 : Thu, Mar 24, 11:00 am-11:50 am
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Exercises | |
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To Be Announced
- Meeting 40 : Fri, Mar 25, 10:00 am-10:50 am
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Exercises | |
Reading | |
To Be Announced
- Meeting 41 : Mon, Mar 28, 08:00 am-08:50 am
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Exercises | |
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To Be Announced
- Meeting 42 : Tue, Mar 29, 12:00 pm-12:50 pm
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Exercises | |
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To Be Announced
- Meeting 43 : Thu, Mar 31, 11:00 am-11:50 am
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Exercises | |
Reading | |
To Be Announced