Software product lines (SPLs) have reached a considerable level of adoption in the software industry. The most commonly used models for managing the variability of SPLs are feature models (FMs). The analysis of FMs is an error-prone, tedious task, and it is not feasible to accomplish this task manually with large-scale FMs.
Today software customers are demanding new and better products and services, which has forced the software industry to devise new approaches that increase the productivity of their processes and the quality of their products. For some time now, researchers in the field of software engineering
have studied various alternatives for software development; among these is the software product lines (SPLs) approach. There are several differences between traditional single-system development and SPLs. The main difference is a paradigm change from individual software systems to a product line (also known as a family product) approach. According to 
, adopting this new paradigm implies a change in strategy: from the ad hoc next-contract vision to a strategic view of a field of business.
SPLs are defined as a set of characteristics to satisfy the specific needs of a particular market segment 
. The use of SPLs as a software development methodology provides a set of benefits, including a reduction in development times and increases in productivity, among others 
. Furthermore, Van der Linden et al. argue that these improvements significantly affect the development process, particularly in relation to costs and time to market, but it is at the level of software reuse that it is possible to achieve unprecedented levels of reuse 
SPL development is based on a common set of fundamental elements: an architecture, a collection of software components, and a set of products 
. One of the key concepts is variability, which provides SPLs with the flexibility required for product diversification and differentiation 
. Variability refers to combining the different functionalities that each component gives to the LPS, and this can be represented graphically using variability models. Nowadays, there are various methods of representing the variability in an LPS; however, feature models (FMs) are the most widely used method 
SPLs and variability are currently a fully active research area, showing their validity and relevance in the software engineering community. This relevance can be seen in a series of tertiary studies, i.e., studies that identify how variability is modeled 
. Additionally, here can see how SPL engineering and variability management has been applied along with the Internet of Things 
Building and maintaining an FM is considered an expensive and error-prone task 
. Moreover, the evolution and changes in the FM can introduce redundancy into the models, leading to the information being modeled in a contradictory way, resulting in modeling errors 
Throughout the SPL framework, starting from the creation of the FMs, the validation of the SPLs, the derivation of products, and even the modification or extension of the product family, it is essential to consult the FMs to obtain relevant information on the processes mentioned above. However, providing answers to these queries is not trivial because, given the structure of FMs, this process requires algorithms that support a set of rules and constraints that tend to be more complex depending on the model’s size. This process of securing information is known as the automated analysis
of feature models
(AAFM), and it has been identified as one of the most critical areas in the SPL community 
. According to 
, it is possible to propose ad hoc algorithms to perform AAFM.
2. Software Product Lines
SPLs are defined as a set of similar software products created from reusable artifacts in the context of a specific application domain 
. SPLs are developed in two stages: domain engineering
and application engineering 
. In the domain engineering
stage, the common and variant elements are described. The application engineering
stage is where the individual products of the SPL are built by reusing domain devices and exploiting the variability of the SPLs. Figure 1
shows the SPL framework, including both stages and their interactions.
Figure 1. SPL framework, stages and their relationships.
Software development based on SPLs has brought about benefits such as the reuse of components, increases in productivity, reductions in development times, relatively fewer major errors, improvements in product quality, and lower costs, among others 
. Contrary to what one may initially believe, the successful implementation of SPLs is not a phenomenon exclusive to large development companies but is also feasible in small and medium-sized companies, as demonstrated in 
One of the main concepts in SPLs development is variability
, which gives SPLs the flexibility required to diversify and differentiate products 
Variability is introduced by defining reusable artifacts, such as architectures or components. These artifacts are included in the definition of a product family, depending on their inclusion or exclusion in each final product, giving rise to particular products 
. Several authors have proposed models to manage the variability of SPLs. Most of these proposals are based on the FODA model 
. This FODA model consists of characteristics and relationships that are graphically extended in the form of a tree.
For example, a software product must be able to adapt to the needs of each client or allow options for some specific configuration so that the products can reach different market segments 
. In domain engineering
, it is common to describe SPL and manage its variability
with the aid of FMs 
4. Feature Models
The origin of FMs can be traced to the FODA method 
. This model is still present but with slight variations and adaptions in some SPL methods based on visual representations of the product’s features.
The structure of an FM is a type of tree of which the root node represents the product family, and the features are organized throughout the tree. These features can be assembled to give rise to particular software products 
. FMs have been a relevant topic for SPLs in recent years, showing the best evolution behavior in terms of the number of published papers and references 
To illustrate the concepts present in an FM, consider the following scenario. A mobile phone must have the possibility of making a call and have a screen, but not all mobile phones must have a GPS. Furthermore, some of these features can depend on others for their inclusion or exclusion. For example, if a mobile phone has a GPS, it cannot have a basic screen. See details in Figure 2.
Figure 2. Example of an FM for a Mobile Phone SPL.
5. Automated Analysis of FMs–Reasoning Algorithms
Automatic analysis of FMs (AAFM) extracts information from such models using automated mechanisms 
. This information includes verifying whether a given product represents a valid combination of features or checking the similarity between FMs. The analysis of FMs is an error-prone, tedious task, and it is not feasible to achieve this task manually with large-scale FMs. AAFM is an active area of research and is gaining importance for both practitioners and researchers in the SPL community 
Benavides et al. mention that AAFM can be defined as the computer-assisted extraction of information from FMs 
. Different proposals for extracting this information have been made, based on specific algorithms or binary decision diagrams, such as BDD, SAT, and CSP 
. Table 1
presents a summary of these proposals.
Table 1. Proposals to extract information from FMs.
The process of extracting information from an FM starts with the translation of the features and relationships encoded in the FMs and any additional information into a knowledge base described in a logical paradigm 
. Subsequently, queries to the knowledge base can be performed using solvers.These operations are performed automatically using different approaches. Most of them translate FMs into specific logical paradigms, such as propositional logic, constraint programming, and description logic 
A classification of different proposals related to automatic or semi-automatic FM construction is presented in 
. The authors of that study conceptualized an analysis framework for work in the field of automated FM construction. The framework considers four dimensions (proposal, input, tasks, and output) and fifteen sub-dimensions.