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a
b
i 2 / u 1
u 1 / v 2
v 2 / u 1
q 0
q 1
t 0
t 1
u 1 / v 1
i 2 / o 2
u 2 / v 1
v 2 / o 2
i 1 / u 2
v 1 / o 1
v 2 / v 1
i 1 / u 1
v 2 / u 2
c
d
u 2 / v 1
i 1 / o 1
u 1 / v 1
i 1 / o 1
u 1 / v 2
s 0
s 2
p 1
p 2
p 3
u 1 / v 2
i 2 / o 2
u 1 / v 1
i 2 / o 1
u 2 / v 1
u 2 /
u 2 / v 2
i 2 / o 2
u 1 /
u 2 / v 1
dc
p 5
p 4
s 1
u 2 / v 2
i 1 / o 2
/
u 2 /
( a ) FSM Context ;( b ) FSM Emb ;( c ) FSM Spec def
Fig. 16.2
D Context ˘ Emb ;( d ) Largest solution
of the equation Context ˘ X Š Spec
that is externally distinguishable from Emb , there exists a sequence in TS int that
distinguishes Imp and Emb . The subset of J Emb that contains FSMs externally
indistinguishable from Emb is characterized by the FSM Largest , therefore, the
problem of generating a complete internal test suite becomes now as follows. Given
the pair J Emb and Largest , we are required to determine a set TS int of input sequences
such that for each FSM Imp 2 J Emb that is not a reduction of the FSM Largest ,
there exists ˛ 2 TS int such that the output response of Imp under the input ˛
cannot be produced by the FSM Largest under ˛ . This problem can be solved
using the method developed in [108] for generating complete test suites for the
case of reduction relation between implementation and specification FSMs. Such
a complete internal test suite can be translated into a complete external test suite
according to Proposition 16.2 .
We illustrate the approach for testing an embedded component using an example
from [114].
Example 16.3. Given the topology in Fig. 16.1 , consider the instances of Context ,
Emb and Spec in Fig. 16.2 a-c; the largest complete solution of the equation
Context ˘
X
Š
Spec is shown in Fig. 16.2 d. FSM Emb is included in Largest ,
 
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