An analysis of the coupling effect I: single test data

The focus in mutation testing is on the elimination of first-order mutants. It is widely believed that there is a coupling effect between first-order and higher-order mutants such that a test set that kills the former would be expected to kill the latter too; it follows that, if the belief is correct, there is no need whatsoever to bother with higher-order mutants. It turns out, in practice, that most higher-order mutants do get killed by such a test set, though a few somehow manage to survive. This is the first of two papers dealing with the coupling effect from a theoretical standpoint. The overall results indicate that the hypothesis of a coupling effect is largely valid, provided the program is not too large; only a tiny proportion of higher-order mutants is expected to survive a test set that kills all first-order mutants. The basis of the approach is that programs can be modelled as compositions of finite functions, the domain of which is assumed to be large. The problem is a complex one, so the present paper only considers the case where there is just one test data; the case where there are more than one test data is left to a second paper. The aim is not only to show that the coupling effect actually exists, but also to gain some understanding of the various factors underlying it.