DONE represents the done moving of elevator.
The faulty process from this graph is the path [s
1
,
s
2
,
s
3
,
s
4
]. The interpretation is: start elevator {s
1
,s
2
}.
In the state s
2
we observed that have not close, that
is the door and it isn’t close, and the moving is out
of order and it pointed some error. Passed from the
state s
2
in the state s
3
where the door elevator shall
be close. In the state s
3
has error and the movement
of elevator don’t start so it shall push the reset
button for the reestablishment. That is, from s
3
passed to the state s
4
. Observed that the process with
normal move in the case view from the original CTL
Kripke structure through [s
1
, s
4
, s
5
, s
6
, s
7
]. Noticed
that this model do not satisfies the property f =
¬EF(St∧EG¬Mv) (Harris, 2003). The CTL model
updated brings a minimum modification of the
Kripke model which satisfies the property f. Firstly,
it should analyze f in AG(¬(St∧EG¬Mv)) for
remove the symbol ¬. The translation is doing with
the function Upd¬. Then is necessary to check each
state whether it satisfies ¬(St∧EG ¬Mv). This string
shall be parsing before it is checked. Selecting the
EG¬Mv to elevator through the model checking
function for EG.
In this model, any path has any state when
¬
Mv
is selected. Here are searched the paths in the form
[s
1
,s
2
,s
3
,s
4
,s
1
,…] and [s
1
,s
4
,s
1
,…] which represent the
connected components loops satisfy EG
¬
Mv. Then
are identified all states with St, these are {s
2
,s
3
,s
5
,s
6
}.
Then are selected the states with St and
¬
Mv, these
are {s
2
,s
3
}. Because the AG(¬(St∧EG¬Mv)) formula
identifies the model don’t have the both states St and
¬
Mv, is necessary an execution with states s
2
and s
3
so it should apply the updated model. From
execution of Upd
AG
function, we shown the case in
which applying P
3
on the state s
2
and s
3
. The first
translate will be from ¬(St∧EG¬Mv) to
¬St∧¬EG¬Mv, therefore s
2
and s
3
are updated with
any ¬St or ¬EG¬Mv by the main function CTLUpd
what is dealt with ∨ and with the Upd
¬
function. In
other words, the new states of s
2
and s
3
shall be
denoting with s
2
′ and s
3
′. The Upd
AG
(M,¬(St∧
EG¬Mv)) function calls the main function
CTLUpd(M,
¬
St) or CTLUpd(M, ¬EG¬Mv) for the
case f
1
∨ f
2
. We choose the ¬St because this is
simplest than ¬EG¬Mv. In this case is necessary to
update the St in states s
2
and s
3
of path π with ¬St
instead, then no states on path π have the
specification EF(St∧EG¬Mv). M ′=(M′,s
1
)╞ ¬EF(St
∧ EG ¬Mv). The state s
2
′
is set {¬St,¬Cl, ¬Mv, Er}
and the state s
3
′
is set {¬St,Cl,¬Mv, Er}.
The algorithm will generate one of the three
resulting models without specific indication, because
criteria used are satisfying all the minimally changes
from the original model. We consider that our
elevator model propose is a model much more
simple for understandable and for implemented,
because we used a steps method to illustrate this
elevator controller. In our case we used the CTL
model checker update, verifying all five properties
mentioned above which are accomplished also in our
case of study.
5 CONCLUSIONS
In this paper, we presented a formal approach for the
update the CTL models. Specification of five
primitives on the CTL Kripke models (Ding, 2006),
define the minimal change criteria of the CTL model
updated. Also in this paper are presented semantics
and the computing property of approach that we
used. The proposed case study is an update principle
of minimal change with maximal reachable states,
which can significantly improve the update results in
modification scenarios of complex system.
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Gomma H., 1993, “Software Design Methods for
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Harris H. and M. Ryan, 2003, ”Theoretical foundations of
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