Anwendungen von #SAT Solvern für Produktlinien: Masterarbeit

Product lines are widely used for managing families of similar products. Typically, product lines are complex and infeasible to analyze manually. In the last two decades, product-line analyses have been reduced to satisfiability problems which are well understood. However, there are methods for which satisfiability is not sufficient. Recently, researchers begun to reduce other problems to #SAT. Yet, only few applications have been considered and those are fairly limited in their scope. Furthermore, the authors mainly propose ad-hoc solutions that are only applicable under certain restrictions or do not scale to large product lines. In this thesis, we aim show the benefits of applying #SAT for the analysis of product lines. To this end, we make the following contributions: First, we summarize applications dependent on #AT considered in the literature and propose new applications to motivate the usage of #SAT technology. Second, we present a variety of algorithms and optimizations for these applications including new proposals. Third, we empirically evaluate 10 proposed algorithms with 14 off-the-shelf #SAT solvers on 131 industrial feature models to identify the fastest algorithms and solvers. Our results show that for each analysis at least one algorithm and solver scale on a vast majority of the feature models, whereas Linux and an automotive model not be analyzed at all. In addition, our results further reveal the benefits of knowledge compilation to deterministic decomposable negation normal form for performing counting-based analyses. Overall, our work shows that #SAT dependent analyses for feature models open a new variety of different applications and scale to a large number of industrial feature models.Produktlinien sind weit verbreitet für die Verwaltung von Familien verwandter Pro- dukte. In der Regel sind Produktlinien komplex und manuell schwer zu analysieren. In den letzten zwei Jahrzehnten wurden Produktlinienanalysen auf Erfüllbarkeit- sprobleme reduziert, für welche es eine Vielzahl an effizienten Werkzeugen gibt. Allerdings ist Erfüllbarkeit nicht für alle Analysen hinreichend. Kürzlich haben Forscher damit begonnen, andere Probleme auf #SAT zu reduzieren. Es wur- den jedoch nur wenige Anwendungen in Betracht gezogen und auch der Anwen- dungsbereich ist begrenzt. Darüber hinaus schlagen die Autoren hauptsächlich Ad-hoc-Lösungen vor, die nur unter bestimmten Einschränkungen der Produktlin- ien anwendbar sind oder nicht für große Produktlinien skalieren. In dieser Arbeit zeigen wir die Vorteile von #SAT Anwendungen für Produtlinien auf. Unser wis- senschaftlicher Beitrag besteht aus den folgenden drei Punkten: Zuerst fassen wir die in der Literatur betrachteten #SAT-Anwendungen zusammen und schlagen neue Anwendungen vor, um den Einsatz von #SAT-Technologien zu motivieren. Zweit- ens stellen wir eine Vielzahl von Algorithmen und Optimierungen für diese Anwen- dungen vor, einschließlich neuer Vorschläge. Drittens führen wir eine empirische Evaluation von 10 der vorgeschlagenen Algorithmen mit 14 #SAT-Solvern auf 131 industriellen Feature-Modellen aus, um die schnellsten Algorithmen und Solver zu identifizieren. Die Ergebnisse der Evaluation zeigen, dass wir für jede Analyse wenig- stens einen Algorithmus und Solver identifiziert haben, die für industrielle Feature- Modelle skalieren. Dazu sind die Ergebnisse ein starker Indikator für die Vorteile des Einsatzes von d-DNNFs bei #SAT-Anwendungen. Insgesamt zeigt unsere Ar- beit, dass #SAT-abhängige Analysen für Feature-Modelle eine Vielzahl neuer un- terschiedlicher Anwendungen ermöglicht und für viele industirelle Feature-Modelle skaliert

Centrality Heuristics for Exact Model Counting

Model counting is the archetypical #P-complete problem consisting of determining the number of satisfying truth assignments of a given propositional formula. In this short paper, we empirically investigate the potential of employing graph centrality measures as a basis of search heuristics in the context of exact model counting. In particular, we integrate centrality-based heuristics into the search-based exact model counter sharpSAT. Our experiments show that employing centrality information significantly improves the empirical performance of sharpSAT, and also allows for simplifying the search heuristics compared to the current default heuristics of the model counter. In particular, we show that the VSIDS heuristic, which is an integral search heuristic employed in essentially all state-of-the-art conflict-driven clause learning Boolean satisfiability solvers, appears to be of very limited use in the context of model counting.Peer reviewe

Reasoning on Feature Models: Compilation-Based vs. Direct Approaches

Analyzing a Feature Model (FM) and reasoning on the corresponding configuration space is a central task in Software Product Line (SPL) engineering. Problems such as deciding the satisfiability of the FM and eliminating inconsistent parts of the FM have been well resolved by translating the FM into a conjunctive normal form (CNF) formula, and then feeding the CNF to a SAT solver. However, this approach has some limits for other important reasoning issues about the FM, such as counting or enumerating configurations. Two mainstream approaches have been investigated in this direction: (i) direct approaches, using tools based on the CNF representation of the FM at hand, or (ii) compilation-based approaches, where the CNF representation of the FM has first been translated into another representation for which the reasoning queries are easier to address. Our contribution is twofold. First, we evaluate how both approaches compare when dealing with common reasoning operations on FM, namely counting configurations, pointing out one or several configurations, sampling configurations, and finding optimal configurations regarding a utility function. Our experimental results show that the compilation-based is efficient enough to possibly compete with the direct approaches and that the cost of translation (i.e., the compilation time) can be balanced when addressing sufficiently many complex reasoning operations on large configuration spaces. Second, we provide a Java-based automated reasoner that supports these operations for both approaches, thus eliminating the burden of selecting the appropriate tool and approach depending on the operation one wants to perform