All-pairs testing について

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All-pairs testing ：ウィキペディア英語版

All-pairs testing
In computer science, all-pairs testing or pairwise testing is a combinatorial method of software testing that, for ''each pair'' of input parameters to a system (typically, a software algorithm), tests all possible discrete combinations of those parameters. Using carefully chosen test vectors, this can be done much faster than an exhaustive search of all combinations of all parameters, by "parallelizing" the tests of parameter pairs.
== Rationale ==

The most common bugs in a program are generally triggered by either a single input parameter or an interactions between pairs of parameters. Bugs involving interactions between three or more parameters are both progressively less common and also progressively more expensive to find---such testing has as its limit the testing of all possible inputs. Thus, a combinatorial technique for picking test cases like all-pairs testing is a useful cost-benefit compromise that enables a significant reduction in the number of test cases without drastically compromising functional coverage.
More rigorously, assume that the test function has

N

parameters given in a set

\ = \

.
The range of the parameters are given by

R(P_i)= R_i

.
Let's assume that

|R_i|= n_i

.
We note that the all possible conditions that can be used is an exponentiation, while imagining that the code deals with the conditions taking only two pair at a time, might reduce the number of conditions.
To demonstrate, suppose there are X,Y,Z parameters.
We can use a predicate of the form

P(X,Y,Z)

of order 3, which takes all 3 as input, or rather three different order 2 predicates of the form

p(u,v)

P(X,Y,Z)

can be written in an equivalent form of

p_(X,Y) ,  p_(Y,Z) , p_(Z,X)

where comma denotes any combination. If the code is written as conditions taking "pairs" of parameters:
then,the set of choices of ranges

X = \

can be a multiset, because there can be multiple parameters having same number of choices.

max(S)

is one of the maximum of the multiset

S

.
The number of pair-wise test cases on this test function would be:-

T =  max(X) \times max ( X \setminus max(X) )

Plainly that would mean, if the

n = max(X)

and

m =  max ( X \setminus max(X) )

then the number of tests is typically O(''nm''), where ''n'' and ''m'' are the number of possibilities for each of the two parameters with the most choices, and it can be quite a lot less than the exhaustive

\prod n_i

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
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