Information Technology Reference
In-Depth Information
≤
≤
Each column of the CA corresponds to a factor or parameter
p
i
(1
i
k
), and
d
i
is called the
level
of
p
i
.
For each parameter/factor, the elements of the domain are not specified explicitly
in the definition. They can be some concrete values like {
John, Mary, …
}or
{
NegativeInt, Zero, PositiveInt
}. They may also be denoted by some
abstract values like {1
}.
Similarly to the case of OAs, some parameters in a CA can be combined when
their levels are the same. If every parameter has the same number of valid values, the
array is called a
fixed level covering array
or simply a
CA
; otherwise, it is called a
mixed level covering array
(MCA) [
11
]. In the former case, we may denote the array
by
CA
,
2
,
3
,...
}or{0
,
1
,
2
,...
d
k
d
k
.
In the literature, some authors put
t
immediately after
N
. They use the notation
CA
(
N
,
,
t
)
, where
d
=
d
1
= ··· =
(
N
;
t
,
d
1
·
d
2
···
d
k
)
. When all the parameters have the same level
v
,theyuse
v
k
CA
.
Note that an OA requires that each
t
-tuple appears exactly the same number of
times. In contrast, a CA only requires that any
t
-tuple appears
at least once
in any
subarray. Thus, an OA is also a CA.
Some examples of (mixed) CAs (with strength
t
(
N
;
t
,
k
,
v
)
or
CA
(
N
;
t
,
)
2) are given in Figs.
1.3
and
1.4
.
CAs like those in Fig.
1.3
are called
binary covering arrays
, because each parameter
can take values from a binary alphabet (usually
=
).
For the MCA in Fig.
1.4
, the first parameter has three possible values, each of the
other parameters is binary (which means, the value is either 0 or 1). If we take any
two columns, say the first column and the last column, we shall see that the subarray
{
0
,
1
}
00
01
11
10
21
20
contains all possible value combinations:
0
,
0
;
0
,
1
;
1
,
0
;
1
,
1
;
2
,
0
;
2
,
1
.
Fig. 1.3
Two instances of
CA
(
5
,
2
4
0000
0111
1011
1101
1110
0001
0010
0100
1000
1111
,
2
)
2
4
Fig. 1.4
MCA
(
6
,
3
·
,
2
)
00000
01111
10011
11100
20101
21010
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