Abstract Family-Based Model Checking Using Modal Featured Transition Systems: Preservation of CTL$$^{\star }$$⋆

Abstract

Variational systems allow effective building of many custom variants by using features (configuration options) to mark the variable functionality. In many of the applications, their quality assurance and formal verification are of paramount importance. Family-based model checking allows simultaneous verification of all variants of a variational system in a single run by exploiting the commonalities between the variants. Yet, its computational cost still greatly depends on the number of variants (often huge). In this work, we show how to achieve efficient family-based model checking of CTL temporal properties using variability abstractions and off-theshelf (single-system) tools. We use variability abstractions for deriving abstract family-based model checking, where the variability model of a variational system is replaced with an abstract (smaller) version of it, called modal featured transition system, which preserves the satisfaction of both universal and existential temporal properties, as expressible in CTL . Modal featured transition systems contain two kinds of transitions, termed may and must transitions, which are defined by the conservative (over-approximating) abstractions and their dual (under-approximating) abstractions, respectively. The variability abstractions can be combined with different partitionings of the set of variants to infer suitable divideand-conquer verification plans for the variational system. We illustrate the practicality of this approach for several variational systems.

Static Analysis of Featured Transition Systems

“…In Fig. 6, we depict an example FTS modelling the behaviour of a configurable vending machine selling soda and tea from [27], an FTS benchmark which was used in numerous publications, among which [5,6,11,30,32,[42][43][44][45]47]. Its feature model can be represented by the formula s ∨ t over the 4 features { f , c, s, t }, thus resulting in 12 products (i.e., 2 4 −4, excluding ∅, { f }, {c}, { f , c}).…”

Family-Based SPL Model Checking Using Parity Games with Variability

“…For one, the efficiency of our approach with respect to related approaches is not easily measured with the elevator case study. While properties ψ 2 and ψ 5 were verified also in [14,15,25,26,35,38], not much can be concluded from the reported running times. First, our model's mCRL2 code was developed from scratch, following the SMV code from [37], and not the fPROMELA code of [14,15,25,26,35,38].…”

“…In this paper, we present efficient family-based SPL model checking of modal μ-calculus formulae on FTSs based on parity games with variability. Years after its introduction [3,14], family-based model checking of SPLs or program families is still a popular topic [10,16,19,[23][24][25][26], including a few game-theoretic approaches based on solving (3-valued) model checking games on featured symbolic automata and on modal transition systems. A parity game is a 2-player turn-based graph game.…”

Efficient static analysis and verification of featured transition systems

“…Vending Machine In Fig. 8, we depict the FTS modelling the behaviour of a configurable vending machine from Classen (2011), an FTS benchmark which was used in ter Beek et al (2019a) and in many other publications (Classen et al , 2013Devroey et al 2014bDevroey et al , 2016bter Beek et al 2015ater Beek et al , 2015bter Beek et al , 2019bCastro et al 2018;Dimovski 2018Dimovski , 2020Dubslaff 2019). It serves a beverage (soda or tea) either for free or upon payment, in which case a compartment is opened for the customer to take the beverage after which it closes again.…”