Towards a Feature mu-Calculus Targeting SPL Verification

Abstract

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.

Family-Based Model Checking with mCRL2

“…We first show how to solve the family-based model-checking problem via an embedding of μL f into mCRL2's modal μ-calculus with data. Then we define a partitioning procedure for μL f that allows us to apply our results from [20]. Next, we evaluate our approach by verifying a number of representative properties over an mCRL2 specification of the minepump SPL benchmark model [8,13,[23][24][25].…”

“…The constant denotes the feature expression that is always true. We now recall FTSs from [13] as a model for SPLs, using the notation of [20]. For states s, t ∈ S, we write s…”

“…There is a growing body of research on customizing model-checking techniques for SPLs. Like our FTS-based proposals [19,20], the CCS-based proposals PL-CCS [2,10] and DeltaCCS [12] are grounded in the μ-calculus. In [26], PL-CCS was proven to be less expressive (in terms of the sets of definable products) than FTSs, while DeltaCCS allows only limited familybased model checking (viz.…”

“…transitions labeled with feature expressions. In [20], we generalized the approach that led to the featureoriented variants fLTL [13] and fCTL [14] of LTL and CTL to the modal μ-calculus by defining μL f , a feature-oriented variant of μL with an FTS semantics obtained by incorporating feature expressions. While μL f paves the way for family-based model checking, so far the logic was without tool support, and it remained unclear whether it could be used effectively to model check FTSs.…”

“…However, there have been earlier proposals for using the μ-calculus to analyze SPLs (cf., e.g., [2,10,12,19,20]). In [19], for instance, mCRL2 and its toolset [21,22] were used for product-based model checking.…”