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We show that if the Boolean hierarchy collapses to level k, then the polynomial hierarchy collapses to BH3(k), where BH3(k) is the k th level of the Boolean hierarchy over Σ2 . This is an improvement over the known results [3], which show that the polynomial hierarchy would collapse to P [O(log . This result is significant in two ways. First, the theorem(More)
This paper is a study of the existence of polynomial time Boolean connective functions for languages. A languageL has an AND function if there is a polynomial timef such thatf(x,y) εL ⇔x εL andy ε L. L has an OR function if there is a polynomial timeg such thatg(x,y) ε⇔xεL oryεL. While all NP complete sets have these functions, Graph Isomorphism, which is(More)
The research presented in this paper is motivated by the following new results on the complexity of the unique satisfiability problem, USAT. • if USAT≡m USAT, then D P = co-D and PH collapses. • if USAT ∈ co-D, then PH collapses. • if USAT has ORω , then PH collapses. The proofs of these results use only the fact that USAT is complete for D under randomized(More)
We study FP NP k , the class of functions that can be computed with nonadaptive queries to an NP oracle. We show that optimization problems stemming from the known NP complete sets, where the optimum is taken over a polynomially bounded range, are hard for FP NP k. This is related to (and, in some sense, extends) work of Chen and Toda CT91]. In addition, it(More)
The Mouse Genome Sequencing Consortium and the RIKEN Genome Exploration Research grouphave generated large sets of sequence data representing the mouse genome and transcriptome, respectively. These data provide a valuable foundation for genomic research. The challenges for the informatics community are how to integrate these data with the ever-expanding(More)
We study FP|| NP , the class of functions that can be computed in polynomial time with nonadaptive queries to an NP oracle. This is motivated by the question of whether it is possible to compute witnesses for NP sets within FP|| NP . The known algorithms for this task all require sequential access to the oracle. On the other hand, there is no evidence known(More)