@MISC{Lutz94weaklyhard, author = {Jack Lutz}, title = {Weakly Hard Problems}, year = {1994} }

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Abstract

A weak completeness phenomenon is investigated in the complexity class E = DTIME(2 linear ). According to standard terminology, a language H is P m -hard for E if the set Pm (H), consisting of all languages A P m H , contains the entire class E. A language C is P m -complete for E if it is P m -hard for E and is also an element of E. Generalizing this, a language H is weakly P m -hard for E if the set Pm (H) does not have measure 0 in E. A language C is weakly P m -complete for E if it is weakly P m -hard for E and is also an element of E. The main result of this paper is the construction of a language that is weakly P m -complete, but not P m -complete, for E. The existence of such languages implies that previously known strong lower bounds on the complexity of weakly P m -hard problems for E (given by work of Lutz, Mayordomo, and Juedes) are indeed more general than the corresponding bounds for P m -hard problems for E. The proof of this result in...