Formalization and Comparison of MCDC and Object Branch Coverage Criteria

This paper presents formal results derived from the COUVERTURE project, whose goal was to develop tools to support structural coverage analysis of uninstrumented safety-critical software. After briefly introducing the project context and explaining the need for formal foundations, we focus on the relationships between machine branch coverage and the DO-178B Modified Condition/Decision Coverage (MCDC) criterion. A thorough understanding of those relationships is important, since it provides the foundation for knowing where efficient execution trace techniques can be used to demonstrate compliance with the MCDC criterion. We first present several conjectures that were tested using Alloy models, then provide a formally verified characterization of the situations when coverage of object control-flow edges implies MCDC compliance.