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On the basis of the above considerations we may conclude that there are two
approaches to the application of the Cartesian product to decompose an algorithm:
•
Decomposition based on the application of the Cartesian product to the set
U
of the
algorithm
Al
g
=
(
. It enables decomposition of an algorithm into component
algorithms, but the component algorithms we obtain are not usually mutually
autonomous. The decomposition itself is in that case easier than the decomposition
presented in the category of algorithms and more often possible in practice. Lack
of autonomy of the component algorithms creates a certain problem, however,
with the use of methods presented in the previous chapters, the autonomy of
component algorithmsmay get and guarantee the possibility of creating component
algorithms, which is of great importance in practice.
U
,
F
)
•
Decomposition realized by the application of the concept of the Cartesian product
concerning the “whole” algorithm
Al
g
considered as an object in the category of
algorithms. As a result, we receive component algorithms that are independent of
one another, which would enable the creation (designing, programming) of the
algorithms independently (in parallel). However, for the problems occurring in
practice the realization of such decomposition of an algorithm into component
algorithms may turn out to be difficult because it requires to the application of the
concept of the Cartesian product to the whole structure which is an algorithm. It is
necessary to meet certain demands (the form of the Cartesian product in the theory
of a category: [1, 93, 152]) which are difficult to provide in practical applications.
Particularly, these difficulties result from the fact that our considerations presented
in this chapter only confirm the possibility of decomposition of an algorithmwithin
the category of algorithms, but they do not provide practical suggestions on how
for a given algorithm (object of a category)
B
we can find algorithms (as objects
of a category)
A
i
, into which we decompose the initial algorithm, that is how the
sets
A
i
or the functions
ˆ
i
should look like (see works on the theory of a category,
for instance [1, 93, 152]).
It cannot be excluded that the development of research on the properties of the
Cartesian product in the theory of the category (and especially its role in the decom-
position of an algorithm in the category of algorithms) may lead to the possibility of
application of algorithm decomposition in practice, on the basis of the application
of the Cartesian product concept to the category of algorithms.
2.8 Summary—Decomposition, Agent, Autonomy
This chapter presented the concept of decomposition of a given algorithm into compo-
nent algorithms. The analysis of the process of decomposition and different methods
of its realization resulted in the concept of an object and an agent, as well as the
agent system. A basic role was played by the analysis of such property as autonomy
and the notion of an autonomous agent and its capability to observe the behaviour of
another agent in the environment, which constitutes a method of gaining autonomy.
