Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Algebra of Fault Tolerance   Every system of any significant size is created by composition from smaller
sub-systems or components. It is thus fruitful to analyze the fault-tolerance
of a system as a function of its composition. In this paper, two basic types of
system composition are described, and an algebra to describe fault tolerance of
composed systems is derived. The set of systems forms monoids under the two
composition operators, and a semiring when both are concerned. A partial
ordering relation between systems is used to compare their fault-tolerance
behaviors.

3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat