Lecture Notes in Computer Science 3472

226 Laura Brandán Briones and Mathias Röhl
(4) Normalize TTTS: Not observable events could not be tested. Therefor, silent
events are elided and delays of these omitted events are added to their fol-
d1,inp,τ,{}
lowing visible events. Each transition sequence of the form q0 −−−−−−−−→
d2,out,a,r
d1+d2,out,a,r
q1 −−−−−−−−→ q2 is replaced by q0 −−−−−−−−→ q2.
Subsequently, the TTTS has to be re-transformed into a deterministic transition
system, since omitting events may have introduced non-determinism.
Note that, normalization is not allowed to remove cycles of silent actions. At
least one of the actions on such a cycle has to be made visible, i.e. the test
view V has to be changed, to get a proper TTTS.
(5) Minimize TTTS: remove all states that are redundant, i.e. all but one that
are in the same visible equivalence class and have the same set of traces.
There might be states that are in the same visible equivalence class but do
not have the same set of visible traces. Such states have to be kept.
� �s0
s0
0, inp, on,
{c := 0
s Asw := s 1 }
� �
,c=0
8, inp, τ,{}
...
� �s0
s0
� �
,c=8
0, inp, on,
{c := 0,
s Asw := s 1 } 0, inp, on, {c := 0, s Asw := s 1 }
2, inp, τ,{}
3, inp, τ,{}
0, inp,
on,
{c := 0,
1, inp,
1, inp,
��s1� � ��s1� � � τ, {}
τ, {} �s1�
,c=0 ,c=1 ,c=2
s0
s0
s0
0, inp, on, {c := 0, sAsw := s1 }
1, inp,
τ, {}
sAsw := s1 }
0, inp, on, {c := 0, sAsw := s1 }
� � �s1
0, inp, on, {c := 0, s Asw := s 1 }
4, inp, τ,{}
s0
� ,c=3
5, inp, τ,{}
1, inp, � ��s1 τ, {}
0, inp, on, {c := 0, s Asw := s 1 }
s0
� ,c=4
0, inp, on, {c := 0, s Asw := s 1 }
1, inp, τ,{}
� �s0
s0
s0
� �
,c=−1
0, out, off ,
{c := −1
s Asw := s 0 }
1, inp, � ��s1� �
τ, {}
,c=5
Fig. 8.11. A TTTS gained from TTS Ms after digitization and label transformation
Example. After digitization the TTS Ms is reduced to a TTTS with 15 states
(cf. Figure 8.11).
Let us now assume a test view V =(P ′ , Var ′ , C ′ , Ch ′ ), where P ′ = {pen},
Var ′ = Var = ∅, C ′ = C = {c}, andCh ′ = Ch = {on, off }. SinceP ′ ⊂ P
does not contain the name of the switch component psw , valuations and resets
of the locations of the Switch become invisible. By using this view, and applying
normalization the set of states can be reduced to contain only 3 states. We get
the TTTS Spec =(Q, L, −→, q0) ,where