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2008

2008

We introduce the boolean hierarchy of k-partitions over NP for k>=3 as a generalization of the boolean hierarchy of sets (i.e., 2… Expand

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2004

2004

We study whether sets inside NP can be reduced to sets with low information content but possibly still high computational… Expand

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1999

1999

Downward translation of equality refers to cases where a collapse of some pair of complexity classes would induce a collapse of… Expand

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Highly Cited

1996

Highly Cited

1996

We show that if the Boolean hierarchy collapses to level $k$, then the polynomial hierarchy collapses to $BH_{3}(k)$, where $BH_… Expand

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Highly Cited

1991

Highly Cited

1991

We study the complexity of decision problems that can be solved by a polynomial-time Turing machine that makes a bounded number… Expand

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1991

1991

Abstract We show that probabilistic polynomial time (PP) is closed under polynomial-time parity reductions. As corollaries, we… Expand

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Highly Cited

1989

Highly Cited

1989

The Boolean Hierarchy I: Structural Properties [J. Cai et al., SIAM J. Comput ., 17 (1988), pp. 1232–252] explores the structure… Expand

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Highly Cited

1988

Highly Cited

1988

It is shown that if the Boolean hierarchy (BH) collapses, then there exists a sparse set S such that ${\text{co-NP}} \subseteq… Expand

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Highly Cited

1988

Highly Cited

1988

In this paper, we study the complexity of sets formed by boolean operations (union, intersection, and complement) on NP sets… Expand

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Highly Cited

1986

Highly Cited

1986

In this paper, we study the complexity of sets formed by boolean operations (∪, ∩, and complementation) on NP sets. These are the… Expand

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