Featured Weighted Automata

Abstract

A featured transition system is a transition system in which the transitions are annotated with feature expressions: Boolean expressions on a finite number of given features. Depending on its feature expression, each individual transition can be enabled when some features are present, and disabled for other sets of features. e behavior of a featured transition system hence depends on a given set of features. ere are algorithms for featured transition systems which can check their properties for all sets of features at once, for example for LTL or CTL properties.Here we introduce a model of featured weighted automata which combines featured transition systems and (semiring-) weighted automata. We show that methods and techniques from weighted automata extend to featured weighted automata and devise algorithms to compute quantitative properties of featured weighted automata for all sets of features at once. We show applications to minimum reachability and to energy properties.

Multifaceted Automated Analyses for Variability-Intensive Embedded Systems

“…Our FWA differs from that of Fahrenberg et al [60]: (i) ours is linked to a PFM to also check structural requirements; (ii) we support parallel composition and consider time as a special weight in that we execute fastest actions first and dynamically update the remaining time delay of other parallel actions to simulate time elapsing; (iii) Fahrenberg et al [60] represents γ → as a partition of the set of variants because their verification algorithm -which is not tooled -relies on matrix representations, whereas ours relies on antichains [73] to scale wrt. the large state space incurred by our evaluation cases.…”

“…In addition to the input models, experts define the NF requirements as constraints and a cost function representing trade-offs between quality attributes. To relate NF requirements with the design space, we rely on feature models with quality attributes [10], [14] for the structural part, and on featured transition systems [22] with added weights [60] for the behavioural part.…”

“…These approaches, however, cannot handle variability and are thus limited to one system at a time. Accordingly, we propose to generate, from our variability-intensive design space, a Featured Weighted Automaton (FWA) [60] -a recent formalism that combines featured transition systems [22] with priced automata [72]. Basically, FWA is a variability-aware, weighted extension of finite state machines where each transition t is annotated with a formula defining (i) which variants can execute t; and (ii) conditional weight values that depend on the variant executing t. This formula, named weighted feature Fig.…”

“…If R is improved, we continue the exploration (L14) and add the successor to R (L15) using a particular union operator that keeps R as an antichain. This is achieved by a split-and-combine algorithm along the lines of [24], [60], which we do not detail due to lack of space. Finally, we return the set of variants F * that can reach s f while minimizing ζ, together with the optimal cost (L21-22).…”

Towards Sampling and Simulation-Based Analysis of Featured Weighted Automata

“…Past research has relied on variability-aware formalism to represent and verify the behaviour of VIS efficiently [2]- [9]. In particular, Featured Weighted Automata (FWA) [10] is a recent formalism able to (i) express system behaviour as a set of execution traces (i.e. sequences of transitions between system states), (ii) restrict the executability of a given transition to specific VIS variants, and (iii) associate distinct quality attributes to the execution of transitions by the variants.…”