56 research outputs found
Derandomizing from Random Strings
In this paper we show that BPP is truth-table reducible to the set of
Kolmogorov random strings R_K. It was previously known that PSPACE, and hence
BPP is Turing-reducible to R_K. The earlier proof relied on the adaptivity of
the Turing-reduction to find a Kolmogorov-random string of polynomial length
using the set R_K as oracle. Our new non-adaptive result relies on a new
fundamental fact about the set R_K, namely each initial segment of the
characteristic sequence of R_K is not compressible by recursive means. As a
partial converse to our claim we show that strings of high
Kolmogorov-complexity when used as advice are not much more useful than
randomly chosen strings
Locally consistent decomposition of strings with applications to edit distance sketching
In this paper we provide a new locally consistent decomposition of strings.
Each string is decomposed into blocks that can be described by grammars of
size (using some amount of randomness). If we take two
strings and of edit distance at most then their block decomposition
uses the same number of grammars and the -th grammar of is the same as
the -th grammar of except for at most indexes . The edit distance
of and equals to the sum of edit distances of pairs of blocks where
and differ. Our decomposition can be used to design a sketch of size
for edit distance, and also a rolling sketch for edit
distance of size . The rolling sketch allows to update the
sketched string by appending a symbol or removing a symbol from the beginning
of the string
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