Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Average Symmetry and Complexity of Binary Sequences   The concept of complexity as average symmetry is here formalised by
introducing a general expression dependent on the relevant symmetry and a
related discrete set of transformations. This complexity has hybrid features of
both statistical complexities and of those related to algorithmic complexity.
Like the former, random objects are not the most complex while they still are
more complex than the more symmetric ones (as in the latter). By applying this
definition to the particular case of rotations of binary sequences, we are able
to find a precise expression for it. In particular, we then analyse the
behaviour of this measure in different well-known automatic sequences, where we
find interesting new properties. A generalisation of the measure to statistical
ensembles is also presented and applied to the case of i.i.d. random sequences
and to the equilibrium configurations of the one-dimensional Ising model. In
both cases, we find that the complexity is continuous and differentiable as a
function of the relevant parameters and agrees with the intuitive requirements
we were looking for.

5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol