2,931 research outputs found
K-trivial, K-low and MLR-low sequences: a tutorial
A remarkable achievement in algorithmic randomness and algorithmic
information theory was the discovery of the notions of K-trivial, K-low and
Martin-Lof-random-low sets: three different definitions turns out to be
equivalent for very non-trivial reasons. This paper, based on the course taught
by one of the authors (L.B.) in Poncelet laboratory (CNRS, Moscow) in 2014,
provides an exposition of the proof of this equivalence and some related
results. We assume that the reader is familiar with basic notions of
algorithmic information theory.Comment: 25 page
Faster 64-bit universal hashing using carry-less multiplications
Intel and AMD support the Carry-less Multiplication (CLMUL) instruction set
in their x64 processors. We use CLMUL to implement an almost universal 64-bit
hash family (CLHASH). We compare this new family with what might be the fastest
almost universal family on x64 processors (VHASH). We find that CLHASH is at
least 60% faster. We also compare CLHASH with a popular hash function designed
for speed (Google's CityHash). We find that CLHASH is 40% faster than CityHash
on inputs larger than 64 bytes and just as fast otherwise
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