Locating P poly Optimally in the Extended Low Hierarchy

The low hierarchy within NP and the extended low hierarchy have turned out to be very useful in classifying many interesting language classes We relocate P poly from the third level EL Balc azar et al to the third level EL of the extended low hierarchy The location of P poly in EL is optimal since as shown by Allender and Hemachandra there exist sparse sets that are not contained in the next lower level EL As a consequence of our result all NP sets in P poly are relocated from the third level L Ko and Sch oning to the third level L P of the low hierarchy

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