A test coverage criterion defines a set E/sub r/ of entities of the program flowgraph and requires that every entity in this set is covered under some test Case. Coverage criteria are also used to measure the adequacy of the executed test cases. In this paper, we introduce the notion of spanning sets of entities for coverage testing. A spanning set is a minimum subset of E/sub r/, such that a test suite covering the entities in this subset is guaranteed to cover every entity in E/sub r/. When the coverage of an entity always guarantees the coverage of another entity, the former is said to subsume the latter. Based on the subsumption relation between entities, we provide a generic algorithm to find spanning sets for control flow and data flow-based test coverage criteria. We suggest several useful applications of spanning sets: They help reduce and estimate the number of test cases needed to satisfy coverage criteria. We also empirically investigate how the use of spanning sets affects the fault detection effectiveness.

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.

Branch coverage is often used to evaluate testing thoroughness. For this reason, it is useful to set a lower bound on the number of test paths needed to achieve branch coverage when estimating how much effort will be needed to test a given program.

Branch testing a program involves generating a set of paths that will cover every arc in the program flowgraph, called a path cover, and finding a set of program inputs that will execute every path in the path cover. This paper presents a generalized algorithm that finds a path cover for a given program flowgraph. The analysis is conducted on a reduced flowgraph, called a ddgraph, and uses graph theoretic principles differently than previous approaches. In particular, the relations of dominance and implication which form two trees of the arcs of the ddgraph are exploited. These relations make it possible to identify a subset of ddgraph arcs, called unconstrained arcs, having the property that a set of paths exercising all the unconstrained arcs also cover all the arcs in the ddgraph. In fact, the algorithm has been designed to cover all the unconstrained arcs of a given ddgraph: the paths are derived one at a time, each path covering at least one as yet uncovered unconstrained arc. The greatest merits of the algorithm are its simplicity and its flexibility. It consists in just visiting recursively in combination the dominator and the implied trees, and is flexible in the sense that it can derive a path cover to satisfy different requirements, according to the strategy adopted for the selection of the unconstrained arc to be covered at each recursive iteration. This feature of the algorithm can be employed to address the problem of infeasible paths, by adopting the most suitable selection strategy for the problem at hand. Embedding of the algorithm into a software analysis and testing tool is recommended.>