P. Beame. A switching lemma primer. Technical report, Department of Computer Science and Engineering, University of Washington, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

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P. Beame. A switching lemma primer. Technical report, Department of Computer Science and Engineering, University of Washington, 1994.

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P. Beame. A switching lemma primer. Technical report, Department of Computer Science and Engineering, University of Washington, 1994.

....the complexity of branching conditions can give an exponential speed up. Our lower bounds are proved using a new kind of switching lemma. A switching lemma provides conditions under which a OR of small ANDs can be rewritten as an AND of small ORs after the application of a random restriction [1, 18, 21, 4]. Our switching lemma differs from previous switching lemmas in that the random restriction is allowed to set a small number of the variables, even as few as n out of n. The trade off is that ORs of extremely small ANDs are transformed into ANDs of modestly small ORs. Therefore, our switching ....

P. Beame. A switching lemma primer. Technical report, Department of Computer Science and Engineering, University of Washington, 1994.

..... This is a substantial improvement over previous lower bounds. Our proof technique applies a switching lemma to a weaker tautology based on certain bipartite graphs. This type of tautology was introduced in [7] Although we rely heavily on the simplified switching lemma arguments presented in [3, 21], in a major difference from previous switching lemma based proofs, both the tautologies themselves and the restrictions we consider remain random throughout most of the argument. 2 Overview The high level schema of our proof is not new. Ignoring parameters for a minute, we start with an alleged ....

....another simple Chernoff bound we show that the degrees of vertices given almost all combinations of graphs and restrictions will not be much larger than their expected value and this suffices to yield the decrease in degree. Overall, our argument is expressed in much the same terms as those in [3, 21], although we find it simpler to omit formally defining k evaluations as separate entities. One way of looking at our technique is that we apply two very different kinds of random restrictions to a proof of n : first, one that sets many variables to 0, corresponding to the restriction of the ....

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P. Beame. A switching lemma primer. Technical Report UW-CSE-95--07--01, Department of Computer Science and Engineering, University of Washington, November 1994.

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