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Robust reductions
 Theory of Computing Systems
, 1999
"... We continue the study of robust reductions initiated by Gavaldà and Balcázar. In particular, a 1991 paper of Gavaldà and Balcázar [7] claimed an optimal separation between the power of robust and nondeterministic strong reductions. Unfortunately, their proof is invalid. We reestablish their theorem ..."
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Cited by 8 (5 self)
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We continue the study of robust reductions initiated by Gavaldà and Balcázar. In particular, a 1991 paper of Gavaldà and Balcázar [7] claimed an optimal separation between the power of robust and nondeterministic strong reductions. Unfortunately, their proof is invalid. We reestablish their theorem. Generalizing robust reductions, we note that robustly strong reductions are built from two restrictions, robust underproductivity and robust overproductivity, both of which have been separately studied before in other contexts. By systematically analyzing the power of these reductions, we
Graph Isomorphism is Low for ZPP(NP) and other Lowness results
, 2000
"... We show the following new lowness results for the probabilistic class ZPP NP . { The class AM \ coAM is low for ZPP NP . As a consequence it follows that Graph Isomorphism and several grouptheoretic problems known to be in AM \ coAM are low for ZPP NP . { The class IP[P=poly], consisting of sets th ..."
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Cited by 7 (0 self)
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We show the following new lowness results for the probabilistic class ZPP NP . { The class AM \ coAM is low for ZPP NP . As a consequence it follows that Graph Isomorphism and several grouptheoretic problems known to be in AM \ coAM are low for ZPP NP . { The class IP[P=poly], consisting of sets that have interactive proof systems with honest provers in P=poly, is also low for ZPP NP . We consider lowness properties of nonuniform function classes, namely, NPMV=poly, NPSV=poly, NPMV t =poly, and NPSV t =poly. Specifically, we show that { Sets whose characteristic functions are in NPSV=poly and that have program checkers (in the sense of Blum and Kannan [8]) are low for AM and ZPP NP . { Sets whose characteristic functions are in NPMV t =poly are low for p 2 .
New Lowness Results for ZPP^NP and other Complexity Classes
, 2000
"... We show that the class AM\coAM is low for ZPP . As a consequence, it follows that Graph Isomorphism and several grouptheoretic problems are low for ZPP . We also ..."
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Cited by 6 (1 self)
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We show that the class AM\coAM is low for ZPP . As a consequence, it follows that Graph Isomorphism and several grouptheoretic problems are low for ZPP . We also
The complexity of unions of disjoint sets
 In Proceedings 24th Symposium on Theoretical Aspects of Computer Science
, 2007
"... This paper is motivated by the open question whether the union of two disjoint NPcomplete sets always is NPcomplete. We discover that such unions retain much of the complexity of their single components. More precisely, they are complete with respect to more general reducibilities. Moreover, we app ..."
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Cited by 2 (2 self)
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This paper is motivated by the open question whether the union of two disjoint NPcomplete sets always is NPcomplete. We discover that such unions retain much of the complexity of their single components. More precisely, they are complete with respect to more general reducibilities. Moreover, we approach the main question in a more general way: We analyze the scope of the complexity of unions of mequivalent disjoint sets. Under the hypothesis that NE � = coNE, we construct degrees in NP where our main question has a positive answer, i.e., these degrees are closed under unions of disjoint sets. 1