Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compression of data streams down to their information content   According to Kolmogorov complexity, every finite binary string is
compressible to a shortest code -- its information content -- from which it is
effectively recoverable. We investigate the extent to which this holds for
infinite binary sequences (streams). We devise a new coding method which
uniformly codes every stream $X$ into an algorithmically random stream $Y$, in
such a way that the first $n$ bits of $X$ are recoverable from the first
$I(X\upharpoonright_n)$ bits of $Y$, where $I$ is any partial computable
information content measure which is defined on all prefixes of $X$, and where
$X\upharpoonright_n$ is the initial segment of $X$ of length $n$. As a
consequence, if $g$ is any computable upper bound on the initial segment
prefix-free complexity of $X$, then $X$ is computable from an algorithmically
random $Y$ with oracle-use at most $g$. Alternatively (making no use of such a
computable bound $g$) one can achieve an oracle-use bounded above by
$K(X\upharpoonright_n)+\log n$. This provides a strong analogue of Shannon's
source coding theorem for algorithmic information theory.

36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys