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TR96-021 | 13th February 1996 00:00
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#### NP-hard Sets Are Superterse unless NP Is Small

**Abstract:**
We show that the class of sets which can be polynomial

time truth table reduced to some $p$-superterse sets has

$p$-measure 0. Hence, no $P$-selective set is $\le_{tt}^p$-hard

for $E$. Also we give a partial affirmative answer to

the conjecture by Beigel, Kummer and Stephan. They conjectured

that every $\le_{tt}^p$-hard set for $NP$ is $P$-superterse

unless $P=NP$. We will prove that every $\le_{tt}^p$-hard set

for $NP$ is $P$-superterse unless $NP$ has $p$-measure $0$.