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Unformatted text preview: Recent advances in Complexity CIS 6930/CIS 4930 October 10, 2002 Lecture 14 Lecturer: Dr. Meera Sitharam Scribe: Erwin Jansen 1 Introduction Today we finished the lower bound proof for monotone functions. Lemma 1. For every monotone circuit C , the number of negative test graphs for which C C does not hold is at most size ( C ) m 2 ( l 2 ) k- 1 p ( k- 1) n Proof. Look at the approximations of and gates and show that at each stage of the construction of C fails. I.e. it gives another output than the original output of or in C in at most m 2 ( ( l 2 ) k- 1 ) p ( k- 1) n negative test graphs. We will start by looking at gates. Consider the gate with two inputs: A = r i =1 d X i e and B = s i =1 d Y i e . From the previous lecture we know that the new approximator is obtained by performing ar most 2 m pluckings on A B . Now we are going to look at how many negative test graphs are destroyed by each plucking. More specifically we will look at the following:each plucking....
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This note was uploaded on 11/09/2011 for the course CIS 6930 taught by Professor Staff during the Fall '08 term at University of Florida.
- Fall '08