A Modal Logic for π-Calculus and Model Checking Algorithm

The π-calculus is one of the most important mobile process calculi and has been well studied in the literatures. Temporal logic is thought as a good compromise between description convenience and abstraction and can support useful computational applications, such as model-checking. In this paper, we use symbolic transition graph inherited from π-calculus to model concurrent systems. A wide class of processes, that is, the finite-control processes can be represented as finite symbolic transition graph. A new version π-μ-Logic is introduced as an appropriate temporal logic for the π-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 the above work, we provide a model checking algorithm for the logic, which follows the well-known Winskel's tag set method to deal with 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.