Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numeration systems on a regular language: Arithmetic operations,
  Recognizability and Formal power series   Generalizations of numeration systems in which N is recognizable by a finite
automaton are obtained by describing a lexicographically ordered infinite
regular language L over a finite alphabet A. For these systems, we obtain a
characterization of recognizable sets of integers in terms of rational formal
series. We also show that, if the complexity of L is Theta (n^q) (resp. if L is
the complement of a polynomial language), then multiplication by an integer k
preserves recognizability only if k=t^{q+1} (resp. if k is not a power of the
cardinality of A) for some integer t. Finally, we obtain sufficient conditions
for the notions of recognizability and U-recognizability to be equivalent,
where U is some positional numeration system related to a sequence of integers.

4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph