Proceedings ArticleDOI
Decision trees and downward closures
Russell Impagliazzo,M. Naor +1 more
- pp 29-38
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The separation of small complexity classes is considered and some downward closure results are derived which show that some intuitively arrive at results that were published previously are misleading.Abstract:
The separation of small complexity classes is considered. Some downward closure results are derived which show that some intuitively arrive at results that were published previously are misleading. This is done by giving uniform versions of simulations in the decision-tree model of concrete complexity. The results also show that sublinear-time computation has enough power to code interesting questions in polynomial-time complexity. >read more
Citations
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Journal ArticleDOI
In search of an easy witness: exponential time vs. probabilistic polynomial time
TL;DR: A number of results are established relating the complexity of exponential-time and probabilistic polynomial-time complexity classes, including NEXP/spl sub/P/poly/spl hArr/NEXP=MA, which can be interpreted to say that no derandomization of MA is possible unless NEXP contains a hard Boolean function.
Proceedings ArticleDOI
CREW PRAMS and decision trees
TL;DR: The results imply that changes in the instruction set of the processors or in the capacity of the shared memory cells do not change by more than a constant factor the time required by a CREW PRAM to compute any Boolean function.
Proceedings ArticleDOI
A note on the power of threshold circuits
TL;DR: The author presents a very simple proof of the fact that any language accepted by polynomial-size depth-k unbounded-fan-in circuits of AND and OR gates is accepted by depth-three threshold circuits of size n raised to the power O(log/sup k/n).
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The Relative Complexity of NP Search Problems
TL;DR: This work proves several separations which show that in a generic relativized world the search classes are distinct and there is a standard search problem in each of them that is not computationally equivalent to any decision problem.
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A uniform approach to define complexity classes
TL;DR: A uniform family of computation models which encompasses most of the complexity classes of interest is introduced and a sufficient and necessary condition for proving separations of relativized complexity classes is given.
References
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Journal ArticleDOI
Relativizations of the $\mathcal{P} = ?\mathcal{NP}$ Question
TL;DR: Relativized versions of the open question of whether every language accepted nondeterministically in polynomial time can be recognized deterministic in poynomial time are investigated.
Journal ArticleDOI
On uniform circuit complexity
TL;DR: It is argued that uniform circuit complexity introduced by Borodin is a reasonable model of parallel complexity and that context-free language recognition is in NC, the class of polynomial size andPolynomial-in-log depth circuits.