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/lp/association-for-computing-machinery/almost-optimal-lower-bounds-for-small-depth-circuits-sENJ5rmLuQ
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- Datasource
- Association for Computing Machinery
- Copyright
- Copyright © 1986 by ACM Inc.
- ISBN
- 0-89791-193-8
- doi
- 10.1145/12130.12132
- Publisher site
- See Article on Publisher Site
Abstract
.Almost O p t i m a l Lower Bounds for S m a l l D e p t h Circuits Johan Hastad * Applied Mathematics department and Laboratory of Computer Science, MIT A b s t r a c t : We give improved lower bounds for the size of small depth circuits computing several functions. In particular we prove almost optimal lower bounds for the size of parity circuits. Further we show that there are functions computable in polynomial size and depth k but requires exponential size when the depth is restricted to k - 1 . Our main lemma which is of independent interest states that by using a random restriction we can convert an AND of small ORs to an OR of small ANDs and conversely. 1. Introduction Proving lower bounds for the resources needed to compute certain functions is one of the most interesting branches of theoretical computer science. One of the ultimate goal of this branch is of course to show that N P ~ P. However, it seems that we arc yet, quite far from achieving this goal and that new techniques have to be developed before we can make