Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The intersection and the union of the asynchronous systems   The asynchronous systems $f$ are the models of the asynchronous circuits from
digital electrical engineering. They are multi-valued functions that associate
to each input $u:\mathbf{R}\to \{0,1\}^{m}$ a set of states $x\in f(u),$ where
$x:\mathbf{R}\to \{0,1\}^{n}.$ The intersection of the systems allows adding
supplementary conditions in modeling and the union of the systems allows
considering the validity of one of two systems in modeling, for example when
testing the asynchronous circuits and the circuit is supposed to be 'good' or
'bad'. The purpose of the paper is that of analyzing the intersection and the
union against the initial/final states, initial/final time, initial/final state
functions, subsystems, dual systems, inverse systems, Cartesian product of
systems, parallel connection and serial connection of systems.

19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th