Almost everywhere high nonuniform complexity
Journal of Computer and System Sciences
Theoretical Computer Science
The Complexity and Distribution of Hard Problems
SIAM Journal on Computing
Almost every set in exponential time is P-bi-immune
Theoretical Computer Science
SIAM Journal on Computing
Genericity and measure for exponential time
MFCS '94 Selected papers from the 19th international symposium on Mathematical foundations of computer science
Resource bounded randomness and weakly complete problems
Theoretical Computer Science
Structural properties of complete problems for exponential time
Complexity theory retrospective II
The quantitative structure of exponential time
Complexity theory retrospective II
A Comparison of Weak Completeness Notions
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Pseudorandom generators, measure theory, and natural proofs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Polynomial reducibilities and complete sets.
Polynomial reducibilities and complete sets.
The cpa's responsibility for the prevention and detection of computer fraud.
The cpa's responsibility for the prevention and detection of computer fraud.
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The resource-bounded measure theory of Lutz leads to variants of the classical hardness and completeness notions. While a set A is hard (under polynomial time many-one reducibility) for a complexity class C if every set in C can be reduced to A, a set A is almost hard if the class of reducible sets has measure 1 in C, and a set A is weakly hard if the class of reducible sets does not have measure 0 in C. If, in addition, A is a member of C then A is almost complete and weakly complete for C, respectively. Weak hardness for the exponential time classes E = DTIME(2lin(n)) and EXP = DTIME(2poly(n)) has been extensively studied in the literature, whereas the nontriviality of the concept of almost completeness has been established only recently. Here we continue the investigation of these measure theoretic hardness notions for the exponential time classes and we establish the relations among these notions which had been left open. In particular, we show that almost hardness for E and EXP are independent. Moreover, there is a set in E which is almost complete for EXP but not weakly complete for E. These results exhibit a surprising degree of independence of the measure concepts for E and EXP. Finally, we give structural separations for some of these concepts and we show the nontriviality of almost hardness for the bounded query reducibilities of fixed norm.