Modal I/O Automata for Interface and Product Line Theories

Alfaro and Henzinger use alternating simulation in a two player game as a refinement for interface automata [1]. We show that interface automata correspond to a subset of modal transition systems of Larsen and Thomsen [2], on which alternating simulation coincides with modal refinement. As a consequence a more expressive interface theory may be built, by a simple generalization from interface automata to modal automata. We define modal I/O automata, an extension of interface automata with modality. Our interface theory that follows can express liveness properties, disallowing trivial implementations of interfaces, a problem that exists for theories build around simulation preorders. In order to further exemplify the usefulness of modal I/O automata, we construct a behavioral variability theory for product line development.