A comparison of polynomial time completeness notions
Theoretical Computer Science
On 1-truth-table-hard languages
Theoretical Computer Science
Theoretical Computer Science
SIAM Journal on Computing
A Comparison of Weak Completeness Notions
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
On the structure of complete sets: Almost everywhere complexity and infinitely often speedup
SFCS '76 Proceedings of the 17th Annual Symposium on Foundations of Computer Science
Weak completeness notions for exponential time
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Nontriviality for exponential time w.r.t weak reducibilities
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Comparing Nontriviality for E and EXP
Theory of Computing Systems - Computability in Europe: Mathematical Theory and Computational Practice
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A set A is nontrivial for the linear exponential time class E=DTIME(2^l^i^n) if A@?E and the sets from E which can be reduced to A are not from a single level DTIME(2^k^n) of the linear exponential hierarchy. Similarly, a set A is nontrivial for the polynomial exponential time class EXP=DTIME(2^p^o^l^y) if A@?EXP and the sets from EXP which can be reduced to A are not from a single level DTIME(2^n^^^k) of the polynomial exponential hierarchy (see [2]). Here we compare the strength of the nontriviality notions with respect to the underlying reducibilities where we consider the polynomial-time variants of many-one, bounded truth-table, truth-table, and Turing reducibilities. Surprisingly, the results obtained for E and EXP differ. While the above reducibilities yield a proper hierarchy of nontriviality notions for E, nontriviality for EXP under many-one reducibility and truth-table reducibility coincides.