Manindra Agrawal, Eric Allender

We show that all sets complete for NC$^1$ under AC$^0$

reductions are isomorphic under AC$^0$-computable isomorphisms.

Although our proof does not generalize directly to other

complexity classes, we do show that, for all complexity classes C

closed under NC$^1$-computable many-one reductions, the sets ...
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Joshua Grochow

Mahaney's Theorem states that, assuming P $\neq$ NP, no NP-hard set can have a polynomially bounded number of yes-instances at each input length. We give an exposition of a very simple unpublished proof of Manindra Agrawal whose ideas appear in Agrawal-Arvind ("Geometric sets of low information content," Theoret. Comp. Sci., ... more >>>