# Reasoning Algorithms on Feature Modeling--A Systematic Mapping Study
## 3 Related Work  
To date and as far as we could ascertain, there have been no other secondary studies dedicated to reviewing the use of reasoning algorithms and FMs. Therefore, this section presents a summary of three proposals related to automated feature modeling analysis [14; 28; 31]. \begin{table}
\begin{tabular}{p{85.4 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Operation** & **Definition** & **Possible Applications** \\ \hline \multirow{2}{*}{
\begin{tabular}{} \end{tabular} } & This operation takes an FM as the input and returns a value indicating whether such model is void. & Automating this operation helps to debug large-scale FMs. \\ \hline \multirow{4}{*}{Valid product} & This operation takes an FM and a product as the input and returns a value that determines whether the product belongs to the set of products represented by the FM or not. & This operation may help tie determine whether a given product is available in an SPL. \\ \hline \multirow{2}{*}{All products} & This operation takes an FM as the input and returns all the products represented by the model. & This operation may help to identify new valid requirement combinations not considered in the initial scope of the SPL. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Examples of analysis operations on FMs. Figure 3: Synthesis of FM data extraction process [30]. \begin{table}
\begin{tabular}{p{85.4 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
\begin{tabular}{} \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of representations of relationships of FMs. Furthermore, we considered an extra systematic review dealing with FM defects and their improvement [32]. The overlapping RQs for the related work are shown in Table 4 (\(\checkmark\) symbol). [PERSON] et al. [14] presented a systematic literature review on the automated analysis of FMs. Their review included 53 papers from 1990 to 2010. The review presented a catalog with 30 analysis operations identified in the literature. It also provided information about the tools used to perform the analyses and the results. The authors concluded that the automated analysis of FMs was maturing, with an increasing number of contributions, operations, tools, and empirical works. They also identified some challenges for future research. [PERSON] et al. [28] present an overview of the evolution of the automated analysis of FMs. The authors performed a systematic mapping study considering 423 papers from 2010 to 2017. The authors found six different facets of variability with the automated analysis of FMs having been applied to product configuration and derivation, testing and evolution, reverse engineering, multi-model variability analysis, variability modeling, and variability-intensive systems. They also confirmed the lack of industrial evidence in most of the cases. Finally, they suggested some synergies with other areas that could motivate further research in the future. [PERSON] [31] presented an overview of the history and the importance of variability modeling and analysis. The author tracesd 30 years of history, from the models proposed by [PERSON] in 1990 [20] to the present day. The work examined the beginnings, evolution, and maturity of variability modeling. This overview included FMs, their formal modeling, and the automatic analysis of variability models. [PERSON] et al. [32] presented a summary and critical research issues related to FM defects in SPL. The authors performed a systematic literature review, considering 77 papers from 1990 to 2015. According to the authors, the paper considered five main contributions. The first was a classification of FM defects in the form of a typology. Then, they presented the identification of various types of FM defects and their explanations. Third, the description, identification, explanation, and formalization of a possible set of cases of FM defects and their sub-case(s) were carried out. Fourth, corrective explanations were proposed to fix defects.