Software Testing Methodologies Dichotomies

Image shows possible domain bugs for a one-dimensional open domain boundary
The closure can be wrong (i.e., assigned to the wrong domain) or the boundary (a point in this case) can be shifted one way or the other, we can be missing a boundary or we can have an extra boundary
In image (a) we assumed that the boundary was to be open for A. The bug we are looking for is a closure error, which converts > to >=  or <= (shown in image (b))
One test, which is marked x on the boundary point, will detect this bug as processing for that point will go to domain A but not to B

In image (c) we have suffered a boundary shift to the left. The test point we used for closure detects this bug because the bug forces the point from the B domain, where it should be, to A processing

Note that we can't distinguish between a shift and a closure error, but we do know that we have a bug

Image (d) shows a shift the other way. The 'on' point does not tell us anything because the boundary shift does not change the fact that the test point will be processed in B

For detecting this shift, a point which is close to the boundary but within A is necessary. As the boundary is open, it can be said by definition that the 'off' point is in A (open off inside)

The same 'off' point also suffices to detect a missing boundary because what should have been processed in A is now processed in B

For detecting an extra boundary, two domain boundaries must be look at. In this context, an extra boundary implies that the boundary A is divided into two

The two 'off' points, one point for each boundary, that were selected will do the job. If the point C is a closed boundary, then the 'on' test point at that point does it

For closed domains, look at display image. As for the open boundary, a test point on the boundary detects the closure bug

The remaining cases of closed boundary are similar to the open boundary, except that the strategy needs 'off' points just outside the domain.