Having test cases that are good at revealing the presence of faults is central to successful testing. Ideally, we would like to determine a set of test cases such that successful execution of all of them implies that there are no errors in the program. This ideal goal cannot usually be achieved due to practical and theoretical constraints.

As each test case costs money, effort is needed to generate the test case, machine time is needed to execute the program for that test case, and more effort is needed to evaluate the results.

Therefore, we would also like to minimize the number of test cases needed to detect errors. These are the two fundamental goals of a practical testing activity – maximize the number of errors detected and minimize the number of test cases. With selecting test cases the primary objectives is to ensure that if there is an error or fault in the program, it is exercised by one of the test cases.

An ideal test case set is one that succeeds (meaning that its execution reveals no errors) only if there are no errors in the program. For this test selection criterion can be used. There are two aspects of test case selection – specifying a criterion for evaluating a set of test cases, and generating a set of test cases that satisfy a given criterion.

There are two fundamental properties for a testing criterion: reliability and validity. A criterion is reliable if all the sets that satisfy the criterion detect the same errors. A criterion is valid if for any error in the program there is some set satisfying the criterion that will reveal the error. Some axioms capturing some of the desirable properties of test criteria have been proposed. The first axiom is the applicability axiom, which states that for every program there exists a test set T that satisfies the criterion.

This is clearly desirable for a general-purpose criterion: a criterion that can be satisfied only for some types of programs is of limited use in testing. The anti extensionality axiom states that there are programs P and Q, both of which implement the same specifications, such that a test set T satisfies the criterion for P but does not satisfy the criterion for Q. This axiom ensures that the program structure has an important role to play in deciding the test cases.

The anti decomposition axiom states that there exists a program P and its component Q such that a test case set T satisfies the criterion for P and T1 is the set of values that variables can assume on entering Q for some test case in T and T1 does not satisfy the criterion for Q. Essentially, the axiom says that just because the criterion is satisfied for the entire program, it does not mean that the criterion has been satisfied for its components.

The anti composition axiom states that there exist program P and Q such that T satisfies the criterion for P and the outputs of P for T satisfy the criterion for Q, but T does not satisfy the criterion for the parts P and Q does not imply that the criterion has been satisfied by the program comprising P, Q. It is very difficult to get a criterion that satisfies even these axioms. This is largely due to the fact that a program may have paths that are infeasible, and one cannot determine these infeasible paths algorithmically as the problem is undecidable.