Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From randomness in two symbols to randomness in three symbols   In 1909 Borel defined normality as a notion of randomness of the digits of
the representation of a real number over certain base (fractional expansion).
If we think the representation of a number over a base as an infinite sequence
of symbols from a finite alphabet $A$, we can define normality directly for
words of symbols of $A$: A word $x$ is normal to the alphabet $A$ if every
finite block of symbols from $A$ appears with the same asymptotic frequency in
$x$ as every other block of the same length. Many examples of normal words have
been found since its definition, being Champernowne in 1933 the first to show
an explicit and simple instance. Moreover, it has been characterized how we can
select subsequences of a normal word $x$ preserving its normality, always
leaving the alphabet $A$ fixed. In this work we consider the dual problem which
consists of inserting symbols in infinite positions of a given word, in such a
way that normality is preserved. Specifically, given a symbol $s$ that is not
present on the original alphabet $A$ and given a word $x$ that is normal to the
alphabet $A$ we solve how to insert the symbol $s$ in infinite positions of the
word $x$ such that the resulting word is normal to the expanded alphabet $A\cup
\{s\}$.

22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas