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and
∀
(
x
1
,
x
2
)
∈
Df
1
:
(
Proj
2
ⓦ
f
1
)(
x
1
,
x
2
)
=
x
2
(2.17)
which can be briefly (informally) denoted by
f
1
:
X
1
×
X
2
ₒ
X
1
.
(2.18)
It means that for the calculation of the transition function
f
1
both states—the state
of the algorithm
Al
g
1
as well as the state of the algorithm
Al
g
2
—are necessary,
however, the calculation of the transition function
f
1
influences only the change of
the state of the algorithm
Al
g
1
and does not have any influence on the state of the
algorithm
Al
g
2
. The schema of this relationship is shown in Fig.
2.7
.
•
The algorithm
Al
g
1
is not autonomous towards the algorithm
Al
g
2
, with
interaction
relationship if for the transition function
f
1
of the algorithm
Al
g
1
the following
relationships occur:
x
2
)
∀
(
x
1
,
x
2
)
∈
Df
1
,(
x
1
,
x
2
)
∈
Df
1
,
:
f
1
(
x
1
,
x
2
)
=
f
1
(
x
1
,
(2.19)
and
∃
(
x
1
,
x
2
)
∈
Df
1
:
(
Proj
2
ⓦ
f
1
)(
x
1
,
x
2
)
=
x
2
(2.20)
which can be briefly (informally) denoted by
f
1
:
X
1
ₒ
X
1
×
X
2
.
(2.21)
It means that for the calculation of the transition function
f
1
only the state of the
algorithm
Al
g
1
is necessary, however, the calculation of the transition function
(a)
(b)
Fig. 2.7
Schema of the relationships between the algorithms; the case when the algorithm
Al
g
1
is not
autonomous
towards the algorithm
Al
g
2
with
inter-information
relationship,
a
for calculat-
ing the transition function
f
1
both states—the state of the algorithm
Al
g
1
as well as the state of
the algorithm
Al
g
2
—are necessary,
b
the calculation of the transition function
f
1
influences only
the change of the state of the algorithm
Al
g
1
, and does not have any influence on the state of the
algorithm
Al
g
2
