Towards a modal logic for π-calculus

The pi-calculus is one of the most important mobile process calculi and has been well studied in literature. Temporal logic is thought of as a good compromise between description convenience and abstraction and can support useful computational applications, such as model-checking. In this paper, we use a symbolic transition graph inherited from pi-calculus to model concurrent systems. A wide class of processes, that is, finite-control processes, can be represented as a finite symbolic transition graph. A new version of modal logic for the pi-calculus, an extension of the modal mu-calculus with Boolean expressions over names, and primitives for name input and output are introduced as an appropriate temporal logic for the pi-calculus. Since we make a distinction between proposition and predicate, the possible interactions between recursion and first-order quantification can be solved. A concise semantics interpretation for our modal logic is given. Based on this work, we provide a model checking algorithm for the logic. This algorithm follows Winskel´s well known tag set method to deal with the fixpoint operator. As for the problem of name instantiating, our algorithm follows the ´on-the-fly´ style, and systematically employs schematic names. The correctness of the algorithm is shown