SEKE 2012 Proceedings - Knowledge Systems Institute

Definition 2: For a set of MSCs M, the domain theory
D i for each co mponent i is defined as: ,
then the pair is in the domain theory D i .
From Definition 2, (" send signal (mine detected)",
"stop") from Figure 3 is in the domain theory. This is used
in [7] to define a method to quantify the states.
In [6], several variables are defined to differentiate the
states of a component. However, it leads to having different
behaviors when producing various behavior models for a
single component. Choosing between these models is hard
as they cannot be compared. In [13], it is proposed to use the
invariant properties of the system to find a unique way of
calculating the state values as described below:
Definition 3: In the finite state machine shown with
tuple Σ , for the final state the
state value is calculated as: , and for
0 < k < f the state value is defined as follows:
i) , if there exist
some j and l such that j is the maximum index that
.
ii) if case i) does n ot hold
but , for some k < .
iii) , if none of the above cases hold.
The value of is related to message that comes after.
For case i), the semantic cause is .
For case ii), is the only semantic cause. Finally,
there is not any semantic cause for case iii). The Order of
messages is used to achieve state values.
The state v alues that are f ound using Definition 3 are
effective for analyzing the system behaviors. After
constructing the FSMs from various scenarios or a sin gle
scenario, to clearly analyze the system behavior, the FSMs
for each co mponent are blended. Therefore, the concept of
identical states is defined as:
Definition 4: For each component i, two states and
form the MSCs m and n (m can be eq ual to n ) are
identical states if any of following holds:
i) j = k for .
ii) .
Following the example in Figure 3, the FSMs are
blended in Figure 4 where states are as signed with
appropriate state values. Initial and final state values are 1.
The presence of identical states in the behavior models
may result in emergent behavior since the component may
be confused when the next message is received. Therefore,
dealing with these issues is an i mportant challenge in
analyzing the behavior models. Once the identical states are
found, the finite state machines are merged by merging the
found identical states. In Figure 3, emergent behavior occurs
for component client control as a result of identical states
and
in MSC m1 when the content of "send
signal" messages are not considered. These identical states
are then merged as shown in Figure 5.
f0
Send signal
f1
motors move forward
Stop motors
f2
f3
Rotate
Figure 5. Merging identical states of FSMs for client control of
MSC m1
IV.
Stop
DETECTING EMERGENT BEHAVIOR
The method proposed in [13] merges all the identical
states without considering whether they may produce
emergent behaviors or not. This is an important issue since
merging the identical states that do not produce emergent
behaviors results in overgeneralization in th e behavior
models. Furthermore, merging all th e identical states takes
too much unnecessary time and resources.
In the FSMs of MSC m1 (Figure 3), identical states
leading to e mergent behavior are shown. These states are
identified and merged in Figures 4 and 5 , respectively. In
Figure 6, another example is considered where the FSM for
MSC m2 (presented in Figure 2) is given. Then, states
values are found and the identical states are identified to be
, and . However, these states do n ot lead to
emergent behaviors as the component never gets confused in
performing the messages. Hence, merging is not necessary.
ff
ff
Send signal(less than 10 km)
V(s m1 1)
motors move forward
V(s m1 2)
Rotate
1
S m2 Send signal (battry has power)
0
S m2 motors move forward
1
S m2 2
Rotate
S m2 3
Send signal(no obstacle detected)
1
Send signal(obstacle detected)
Send signal(mine detected)
V(s m1 1)
stop motors
V(s m1 2)
Stop
1
S m2 Send signal (no mine detected)
Rotate
7 S m2 6 S m2 5
motors move forward
S m2 4
motors move forward
V(s m1 1)
stop motors
V(s m1 2)
Stop
1
S m2 8
Rotate
S m2 f
Figure 4. Blending FSMs for client control of MSC m1
Figure 6. FSM for component client control of MSC m2
72