Characteristic mu-Calculus Formulas for Underspecified Transition Systems

Underspecification, which is essential for specification formalisms, is usually expressed by equivalences, simulations, or logic approaches. We introduce underspecified transition systems (UTSs) as general model general model for underspecification, where, e.g., transitions point to sets of states. We argue for the generality of the UTSs by showing that the class of all UTSs is strictly more expressive than the standard equivalences and simulation approaches, in the sense that more sets of transition systems can be expressed. Additionally, a characteristic formula in terms of the μ-calculus is presented for every finite state UTS. Furthermore, we show that UTSs can finitely describe sets of transition systems, whenever they can be described finitely by the other standard approaches except for trace-set extension or μ-calculus descriptions.