Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
SIAM Journal on Computing
Structural complexity 2
Downward translations of equality
Theoretical Computer Science
On random reductions from sparse sets to tally sets
Information Processing Letters
Separating Nondeterministic Time Complexity Classes
Journal of the ACM (JACM)
Isolation, matching and counting uniform and nonuniform upper bounds
Journal of Computer and System Sciences
Resource-Bounded Kolmogorov Complexity Revisited
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
SOFSEM '97 Proceedings of the 24th Seminar on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
NL-printable sets and nondeterministic Kolmogorov complexity
Theoretical Computer Science - Logic, language, information and computation
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In this paper a new upward separation technique is developed. It is applied to prove that for a class of functions F a separation DTIME (F) NTIME (F) can be characterized by the existence of (not only polynomially) sparse sets in certain complexity classes. As a consequence, a solution of an open question of J. Hartmanis (1983, Inform. Process. Lett. 16, 55-60) is obtained: There is an no log n-sparse set in NP-P iff ). Further we prove that there is an no (log n)-sparse set in NP-coNP iff. The technique also allows us to characterize the existence of sets of different densities in NP-P by the existence of slightly denser sets in NTIME (F)-DTIME (F) for certain classes of functions F. For example, there is an no (log n)-sparse set in NP-P iff there is an n0 ((log n)3) -sparse set in. The end of the paper is devoted to limitations of the technique. Copyright 2001 Academic Press.