Invitation Invitation Secret Secret 1 1 Algorithms Algorithms are are at at the the heart heart
of of complexity complexity theory. theory. That That is is the the dark dark secret secret of of …

In his seminal paper on probabilistic Turing machines, Gill [9] asked whether the class PP is
closed under intersection and union. We give a positive answer to this question. In fact, PP is …

We study the complexity of decision problems that can be solved by a polynomial-time
Turing machine that makes a bounded number of queries to an NP oracle. Depending on …

Much structural work on NP-complete sets has exploited SAT′ s d-self-reducibility. In this
paper, we exploit the additional fact that SAT is a d-cylinder to show that NP-complete sets …

The characterizations of the class Theta/sub 2//sup p/of languages polynomial-time truth-
table reducible to sets in NP are surveyed studying the classes obtained when the …

Direct product results and the GCD problem, in old and new communication models Page 1
Direct Product Results and the GCD Problem, in Old and Xew- Communication N1odels Itzhak …

This paper studies a notion called polynomial-time membership comparable sets. For a
function g, a set A is polynomial-time g-membership comparable if there is a polynomial-time …

Let A be a subset of the natural numbers, and let FA n (x 1,..., xn)=< χ A (x 1),..., χ A (xn)>,
where χ A is the characteristic function of A. An oracle Turing machine with oracle A could …

Chang and Kadin have shown that if the difference hierarchy over NP collapses to level k,
then the polynomial hierarchy (PH) is equal to the k th level of the difference hierarchy over Σ …

In this paper we study the complexity of sets that reduce to sparse sets (and tally sets), and
the complexity of the simplest sparse sets to which such sets reduce. We show even with …