Agent Versus Decomposition of an Algorithm - A Perspective on Agent Systems - page 23

Similarly the notion of autonomy of a given algorithm may be considered only
towards another algorithm. For example, the autonomy of the algorithm Al g 1 may
be considered towards the algorithm Al g 2 .
We may then, as in Sect. 2.4.2 , introduce the following cases of the autonomy
of the algorithm Al g 1 towards the algorithm Al g 2 , which both cooperate through
the environment X 0 , taking into consideration the influence of the algorithm on this
environment (simplified informal notation has been applied to formulas):

• The algorithm Al g 1 is autonomous if the function f 1 has the following form:

f 1 : X 0 × X 1 ₒ X 0 × X 1 (2.34)

It means that for the calculation of the transition function f 1 only the state of the
algorithm Al g 1 and the state of the environment X 0 are necessary and the state of
the algorithm Al g 2 is not necessary at all. However, the calculation of the transition
function f 1 influences only the change of state of the algorithm Al g 1 and the state
of the environment X 0 , and does not influence the state of the algorithm Al g 2 .

• The algorithm Al g 1 is not autonomous with inter-information relationship towards

the algorithm Al g 2 if the function f 1 has the following form:

f 1 : X 0 × X 1 × X 2 ₒ X 0 × X 1 (2.35)

It means that for the calculation of the transition function f 1 the state of the algo-
rithm Al g 1 , the state of the algorithm Al g 2 and the state of the environment X 0 are
necessary. However, the calculation of the transition function f 1 influences only
the change of state of the algorithm Al g 1 and the state of the environment X 0 and
does not influence the state of the algorithm Al g 2 .

• The algorithm Al g 1 is not autonomous with inter-action relationship towards the

algorithm Al g 2 if the function f 1 has the following form:

f 1 : X 0 × X 1 ₒ X 0 × X 1 × X 2 (2.36)

It means that for the calculation of the transition function f 1 only the state of the
algorithm Al g 1 and the state of the environment X 0 are essential and the state of the
algorithm Al g 2 is not necessary at all. However, the calculation of the transition
function f 1 influences the change of state of the algorithm Al g 1 , the state of the
algorithm Al g 2 and the state of the environment X 0 .

• The algorithm Al g 1 is not autonomous with inter-operation relationship towards

the algorithm Al g 2 (or completely non-autonomous) if the function f 1 has the
following form:

f 1 : X 0 × X 1 × X 2 ₒ X 0 × X 1 × X 2 (2.37)

It means that for the calculation of the transition function f 1 the state of the algo-
rithm Al g 1 , the state of the algorithm Al g 2 and the state of the environment X 0
are essential. However, the calculation of the transition function f 1 influences the