130 research outputs found
Separation of two-query-adaptive from two-query-non-adaptive completeness if NP is not small
Under the hypothesis that NP does not have p-measure O (roughly, that
NP contains more than a negligible subset of exponential time), it is shown that there is a language that is ≤ P/2-T complete but not ≤ P/2-tt complete for NP. This conclusion, widely believed to be true, is not known to follow from P ≠NP or other traditional complexity-theoretic hypotheses. This is a very preliminar version
Pushdown Compression
The pressing need for eficient compression schemes for XML documents has
recently been focused on stack computation [6, 9], and in particular calls for
a formulation of information-lossless stack or pushdown compressors that allows
a formal analysis of their performance and a more ambitious use of the stack in
XML compression, where so far it is mainly connected to parsing mechanisms. In
this paper we introduce the model of pushdown compressor, based on pushdown
transducers that compute a single injective function while keeping the widest
generality regarding stack computation. The celebrated Lempel-Ziv algorithm
LZ78 [10] was introduced as a general purpose compression algorithm that
outperforms finite-state compressors on all sequences. We compare the
performance of the Lempel-Ziv algorithm with that of the pushdown compressors,
or compression algorithms that can be implemented with a pushdown transducer.
This comparison is made without any a priori assumption on the data's source
and considering the asymptotic compression ratio for infinite sequences. We
prove that Lempel-Ziv is incomparable with pushdown compressors
ALMOST-R: characterizations using different concepts of randomness
We study here the classes of the form ALMOST-R, for R a reducibility. This
includes among other the classes BPP, P and PH. We give a characterization of this
classes in terms of reducibility to n-random languages, a subclass of algorithmically
random languages. We also give a characterization of classes of the form ALMOST-R
in terms of resource bounded measure, for R reducibility of a restricted kind
Computing absolutely normal numbers in nearly linear time
A real number x is absolutely normal if, for every base b ≥ 2, every two equally long strings of digits appear with equal asymptotic frequency in the base-b expansion of x. This
paper presents an explicit algorithm that generates the binary expansion of an absolutely normal number x, with the nth bit of x appearing after npolylog(n) computation steps. This speed is achieved by simultaneously computing and diagonalizing against a martingale that incorporates Lempel-Ziv parsing algorithms in all bases
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