Locating P/poly optimally in the extended low hierarchy

Abstract

The low hierarchy in NP and the extended low hierarchy have turned out to be very useful in classifying many interesting language classes, and almost all of them could be located optimally therein. However, until now, the exact location of P/poly remained open. We show that P/poly is contained in the third theta level (formula presented) of the extended low hierarchy. Since Allender and Hemachandra have shown that there exist sparse sets outside of (formula presented), this is optimal.