Istituto di Scienza e Tecnologie dell'Informazione     
Bertolino A., Marre' M. How many paths are needed for branch testing?. In: Journal of Systems and Software, vol. 35 (2) pp. 95 - 106. Elsevier, 1996.
A bound on the number of test cases needed to achieve branch coverage is important to evaluate the effort needed to test a given program. However, the bounds proposed so far in the Iiterature are not effective to measure testing effort. In this article, we introduce a new, meaningful lower bound on the number of test cases needed to achieve branch coverage. We first identify the set of unconstrained arcs in a ddgraph. This is the minimum set of arcs such that a set of paths that exercises these arcs covers ali the arcs in the program ddgraph. In generai, a path may cover more than one unconstrained are: the strategy we use to combine more unconstrained arcs into one path determines the cardinality of the set of test paths. i.e., the bound we are looking for. It is now commonly accepted that the real problem in branch testing is to derive an executable set of test paths. Therefore, we will consider those control flow paths containing a low number of decisions to be meaningful because they are more Iikely to be feasible. We formalize this notion by introducing the weak incomparability relation between ddgraph arcs. We then define the new, rneaningful bound as the maximum number of unconstrained arcs in a ddgraph that are mutually weakly incomparable. Furthermore, we show that the bound fits into the testability model of Bache and Mùllerburq (1990). © 1996 by Elsevier Scienee Inc.
DOI: 10.1016/0164-1212(95)00089-5

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