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(a)
(b)
(c)
Fig. 2.15
Schema of two approaches to the problemof decomposition of an algorithm:
a
the schema
of a column
i
corresponding to the parameter
X
i
,
b
linear division leading to decomposition into
subprograms,
c
column decomposition being the basis of the concept of the object and the agent
x
i
1
,
x
i
2
,...,
x
i
m
,)
corre-
sponding to the individual states
u
i
, which may be presented as a table form, shown
in Fig.
2.15
a. Both approaches—decomposition based on the division of the set and
decomposition based on the Cartesian product concept—may be presented in the
form of two kinds of division of the table (Fig.
2.15
):
The set
X
may be presented as the lines of the parameters
(
•
Method of decomposition, based on the
linear
division of the table of parameters
(Fig.
2.15
b). This method of decomposition based on the concept of division of
the set
U
and
F
leads to the concept of a subprogram.
•
The
column
decomposition of the table of parameters inspired by the notion of
the Cartesian product (Fig.
2.15
c) provides a basis for the decomposition of an
algorithmwith the use of the concept of an object as well as the concept of an agent.
Summing up, we consider two methods of decomposition—
linear
decomposition
leading to the notion of a subprogram, and
column
decomposition that makes it
possible to define the notion of an object and the notion of an agent.
Using both methods we may define the manner of decomposition of an algorithm
that leads to receiving the multi-agent system.
This process may be realized as follows:
Let us consider the algorithm
Al
g
=
(
. The set of states of this algorithm
U
may be presented as the Cartesian product of the sets of parameters—in other words,
the set
X
, where
X
U
,
F
)
X
n
given in the table form (Fig.
2.16
a). When
analyzing the table, we will present the way of constructing the multi-agent system.
=
X
1
×
X
2
×···×
