Unconstrained duals and their use in achieving all-uses coverage

Testing takes a considerable amount of the time and resources spent on producing software. It would therefore be useful to have ways 1) to reduce the cost of testing and 2) to estimate this cost. In particular, the number of tests to be executed is an important and useful attribute of the entity "testing effort". All-uses coverage is a data flow testing strategy widely researched in recent years. In this paper we present spanning sets of duas for the all-uses coverage criterion. A spanning set of duas is a minimum set of duas (definition-use associations) such that a set of test paths covering them covers every dua in the program. We give a method to find a spanning set of duas using the relation of subsumption between duas. Intuitively, there exists a natural ordering between the duas in a program: some duas are covered more easily than others, since coverage of the former is automatically guaranteed whenever the latter are covered. Those duas that are the most difficult to be covered according to this ordering are called unconstrained. A spanning set of duas is composed of unconstrained duas. Our results are useful for reducing the cost of testing, since the generation of test paths can be targeted to cover the smaller spanning set of duas, rather than all those in a program. On the other hand, assuming that a different path is taken to cover each dua in a spanning set, the cardinality of spanning sets can be used to estimate the cost of testing. Other interesting uses of spanning sets of duas are also discussed.