Now, take a test input <math> I_t </math>, which generates the output <math>I_tO_t</math>, that is the test tuple <math>\tau = (I_t,O_t) </math>. Now, the question is whether or not <math> \tau \in \Sigma </math> or <math> \tau \not \in \Sigma </math>. If it is in the set, the test tuple <math> \tau </math> passes, else the system fails the test input. Therefore, it is of imperative importance to figure out : can we or can we not create a function that effectively translates into the notion of the set [[indicator function]] for the specification set <math> \Sigma </math>.
By the notion, <math>1_{\Sigma}</math> is the testability function for the specification <math>\Sigma</math>.
