Making Hard Problems Harder

Joshua Buresh-Oppenheim, Rahul Santhanam

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a general approach to the hoary problem of (im)proving circuit lower bounds. We define notions of hardness condensing and hardness extraction, in analogy to the corresponding notions from the computational theory of randomness. A hardness condenser is a procedure that takes in a Boolean function as input, as well as an advice string, and ouputs a Boolean function on a smaller number of bits which has greater hardness as measured in terms of input length. A hardness extractor takes in a Boolean function as input, as well as an advice string, and ouputs a Boolean function defined on a smaller number of bits which has close to maximum possible hardness. We prove several positive and negative results about these objects.
Original languageEnglish
Number of pages27
JournalElectronic Colloquium on Computational Complexity (ECCC)
Issue number003
Publication statusPublished - 2006

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