Complete model-based equivalence class testing

In this article, we present a model-based black-box equivalence partition testing strategy, together with a formal proof of its completeness properties. The results apply to reactive systems with large, possibly infinite input data types and finite internal and output data ranges that may be enumerated with acceptable effort. The investigation is performed on a semantic level and applies to all concrete test models whose behavioural semantics can be encoded as a variant of state transition systems. Test suite construction is performed in relation to a given fault model F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{F}$$\end{document} for which a finite black-box test suite can be constructed which is complete with respect to F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{F}$$\end{document}. It is shown how the test suite generation can be effectively implemented by model-based testing tools, using propositional representations of behavioural model semantics and constraint solvers. A SysML model of the ceiling speed monitoring function of the European Train Control System is presented as a case study, to explain theory application to a concrete modelling formalism.