On the relationship between two control-flow coverage criteria: all JJ-paths and MCDC

Coverage criteria may be used to assess the adequacy of software test data. Improved test data, that takes account of any inadequacies identified by lack of coverage, may then be developed. It is natural to seek ways of comparing different criteria and the ‘subsumes’ relationship is one such way: one criterion subsumes another, if satisfying the first always implies satisfaction of the second. This paper considers two criteria: ‘all jump-to-jump paths’ (all JJ-paths) and ‘modified condition/decision coverage’ (MCDC). It might be anticipated that there would be a relationship between these criteria since both are based on advanced control-flow concepts. MCDC has particular importance since it is involved in the DO-178B standard for avionics software. However, it is shown that ‘all JJ-paths’ and MCDC are, in general, incomparable, but for programs written under certain specific constraints ‘all JJ-paths’ subsumes MCDC.