Resource-bounded kolmogorov complexity revisited
We take a fresh look at CD complexity, where CDt(x) is the smallest program that distinguishes x from all other strings in time t(¦x¦). We also look at a CND complexity, a new nondeterministic variant of CD complexity.
Showing how to approximate the size of a set using CD complexity avoiding the random string needed by Sipser. Also we give a new simpler proof of Sipser's lemma.
A proof of the Valiant-Vazirani lemma directly from Sipser's earlier CD lemma.
A relativized lower bound for CND complexity.
Exact characterizations of equivalences between C, CD and CND complexity.
Showing that a satisfying assignment can be found in output polynomial time if and only if a unique assignment can be found quickly. This answers an open question of Papadimitriou.
New Kolmogorov-based constructions of the following relativized worlds:
There exists an infinite set in P with no sparse infinite subsets in NP.
EXP=NEXP but there exists a nondeterministic exponential time Turing machine whose accepting paths cannot be found in exponential time.
Satisfying assignment cannot be found with nonadaptive queries to SAT.
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