Modal and mixed specifications: key decision problems and their complexities

Abstract

Modal and mixed transition systems are specification formalisms that allow the mixing of over- and under-approximation. We discuss three fundamental decision problems for such specifications: —whether a set of specifications has a common implementation;—whether an individual specification has an implementation; and—whether all implementations of an individual specification are implementations of another one. For each of these decision problems we investigate the worst-case computational complexity for the modal and mixed cases. We show that the first decision problem is EXPTIME-complete for both modal and mixed specifications. We prove that the second decision problem is EXPTIME-complete for mixed specifications (it is known to be trivial for modal ones). The third decision problem is also shown to be EXPTIME-complete for mixed specifications.