552 research outputs found
Linear list-approximation for short programs (or the power of a few random bits)
A -short program for a string is a description of of length at
most , where is the Kolmogorov complexity of . We show that
there exists a randomized algorithm that constructs a list of elements that
contains a -short program for . We also show a polynomial-time
randomized construction that achieves the same list size for -short programs. These results beat the lower bounds shown by Bauwens et al.
\cite{bmvz:c:shortlist} for deterministic constructions of such lists. We also
prove tight lower bounds for the main parameters of our result. The
constructions use only ( for the polynomial-time
result) random bits . Thus using only few random bits it is possible to do
tasks that cannot be done by any deterministic algorithm regardless of its
running time
Characterizing small depth and small space classes by operators of higher types
Motivated by the question of how to define an analog of interactive proofs in the setting of logarithmic time- and space-bounded computation, we study complexity classes defined in terms of operators quantifying over oracles. We obtain new characterizations of NC1, L, NL, NP, and NSC (the nondeterministic version of SC). In some cases, we prove that our simulations are optimal (for instance, in bounding the number of queries to the oracle)
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