On determinism in modal transition systems

Modal transition system (MTS) is a formalism which extends the classical notion of labelled transition systems by introducing transitions of two types: must transitions that have to be present in any implementation of the MTS and may transitions that are allowed but not required. The MTS framework has proved to be useful as a specification formalism of component-based systems as it supports compositional verification and stepwise refinement. Nevertheless, there are some limitations of the theory, namely that the naturally defined notions of modal refinement and modal composition are incomplete with respect to the semantic view based on the sets of the implementations of a given MTS specification. Recent work indicates that some of these limitations might be overcome by considering deterministic systems, which seem to be more manageable but still interesting for several application areas. In the present article, we provide a comprehensive account of the MTS framework in the deterministic setting. We study a number of problems previously considered on MTS and point out to what extend we can expect better results under the restriction of determinism.