Towards a feature mu-calculus targeting SPL verification

The modal μ-calculus μL is a well-known fixpoint logic to express and model check properties interpreted over labeled transition systems. In this paper, we propose two variants of the μ-calculus, μL_f and μL?_f, for feature transition systems. For this, we explicitly incorporate feature expressions into the logics, allowing operators to select transitions and behavior restricted to specific products and subfamilies. We provide semantics for μL_f and μL?_f and relate the two new μ-calculi and μL to each other. Next, we focus on the analysis of SPL behavior and show how our formalism can be applied for product-based verification with μL_f as well as family-based verification with μL?_f. We illustrate by means of a toy example how properties can be model checked, exploiting an embedding of μL?_f into the μ-calculus with data.