Incremental satisfiability (SAT) solving is an extension of classic SAT solving that enables solving a set of related SAT problems by identifying and exploiting shared terms. However, using incremental solvers effectively is hard since performance is sensitive to the input order of subterms and results must be tracked manually. For analyses that generate sets of related SAT problems, such as those in software product lines, incremental solvers are either not used or their use is not clearly described in the literature. This paper translates the ordering problem to an encoding problem and automates the use of incremental solving. We introduce variational SAT solving, which differs from incremental solving by accepting all related problems as a single variational input and returning all results as a single variational output. Variational solving syntactically encodes differences in related SAT problems as local points of variation. With this syntax, our approach automates the interaction with the incremental solver and enables a method to automatically optimize sharing in the input. To evaluate these ideas, we formalize a variational SAT algorithm, construct a prototype variational solver, and perform an empirical analysis on two real-world datasets that applied incremental solvers to software evolution scenarios. We show, assuming a variational input, that the prototype solver scales better for these problems than four off-the-shelf incremental solvers while also automatically tracking individual results.
Product lines are widely used to manage families of products that share a common base of features. Typically, not every combination (configuration) of features is valid. Feature models are a de facto standard to specify valid configurations and allow standardized analyses on the variability of the underlying system. A large variety of such analyses depends on computing the number of valid configurations. To analyze feature models, they are typically translated to propositional logic. This allows to employ SAT solvers that compute the number of satisfying assignments of the propositional formula translated from a feature model. However, the SAT problem is generally assumed to be even harder than SAT and its scalability when applied to feature models has only been explored sparsely. Our main contribution is an investigation of the performance of off-the-shelf SAT solvers on computing the number of valid configurations for industrial feature models. We empirically evaluate 21 publicly available SAT solvers on 130 feature models from 15 subject systems. Our results indicate that current solvers master a majority of the evaluated systems (13/15) with the fastest solvers requiring less than one second for each successfully evaluated feature model. However, there are two complex systems for which none of the evaluated solvers scales. For the given experiment design, the solvers that consumed the least runtime are (2.5 seconds in sum for the 13 systems) and (3.5 seconds).
Graphic Data Systems Corporation (GDS Corp.) and Intelligent Graphics Solutions, Inc. (IGS) combined talents in 1995 to design and develop a MicroGDS' application to support field investigations of crime scenes, such as homicides, bombings, and arsons. IGS and GDS Corp. prepared design documents under the guidance of federal, state, and local crime scene reconstruction experts and with information from the FBI's evidence response team field book. The application was then developed to encompass the key components of crime scene investigation: staff assigned to the incident, tasks occurring at the scene, visits to the scene location, photographs taken of the crime scene, related documents, involved persons, cataloged evidence, and two-or three-dimensional crime scene reconstruction. Crime Scene Investigation, Reporting, and Reconstruction (CSIRR©) provides investigators with a single application for both capturing all tabular data about the crime scene and quickly rendering a sketch of the scene. Tabular data is captured through intuitive database forms, while MicroGDSTh has been modified to readily allow non-CAD users to sketch the scene.
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