Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the decomposition of k-valued rational relations   We give a new, and hopefully more easily understandable, structural proof of
the decomposition of a $k$-valued transducer into $k$ unambiguous functional
ones, a result established by A. Weber in 1996. Our construction is based on a
lexicographic ordering of computations of automata and on two coverings that
can be build by means of this ordering. The complexity of the construction,
measured as the number of states of the transducers involved in the
decomposition, improves the original one by one exponential. Moreover, this
method allows further generalisation that solves the problem of decomposition
of rational relations with bounded length-degree, which was left open in
Weber's paper.

12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga