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ABSTRACT: A language A is said to be Pclose if there exists a B in P such that the symmetric difference of A and B forms a sparse set. (A set is sparse if it contains only polynomially many elements up to length n). In this paper the notion of Pcloseness is further generalized to arbitrary classes C. Several results of the following general pattern are shown: No NPhard set can be Cclose unless NP = C. SIAM Journal on Computing 04/1994; 23:255260. · 0.76 Impact Factor

Mathematical Systems Theory 01/1994; 27:183186.

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ABSTRACT: The possibility and consequences are studied of having an NPhard set that forms a symmetric difference with an “easy” set (like a weakly pselective set) that is of “low information content”. Especially, it is shown that the existence of an NPhard set A (with respect to many one reducibility) that forms a symmetric difference to a weakly p selective set B, such that both AB and BA are boundedtruthtable reducible to a sparse set implies P=NP. The proof is based on the tree pruning techniques by Mahaney and Fortune. Theoretical Computer Science 11/1993; 120:279291. · 0.52 Impact Factor

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ABSTRACT: The difference between NP and other complexity classes is
examined. The question of whether an NPhard set can be approximated
sufficiently by the sets in other complexity classes is studied Structure in Complexity Theory Conference, 1992., Proceedings of the Seventh Annual; 07/1992

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ABSTRACT: The authors separate NE from P<sub>x</sub> (NP), where x =
n <sup>0(1)</sup> T . The class EXPlow[1] is introduced
and applied in the investigations of stable properties for both EXP and
NEXP hard sets. A set A is in EXPlow[1](EXPlow resp.) if EXP
<sup>A[1]</sup>=EXP(EXP<sup>A</sup>=EXP). The authors separate
EXPlow[1] from EXPlow by constructing a set A such that EXP
<sup>A[1]</sup>=EXP and EXP<sup>A</sup>=EXP<sup>EXP</sup> Structure in Complexity Theory Conference, 1992., Proceedings of the Seventh Annual; 07/1992

Algorithms and Computation, Third International Symposium, ISAAC '92, Nagoya, Japan, December 1618, 1992, Proceedings; 01/1992