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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Feature Model Synthesis</title>
<meta name="description" content="PhD Thesis Presentation">
<meta name="author" content="Steven She">
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<body>
<div class="reveal">
<p class="slide-number"></p>
<!-- Any section element inside of this container is displayed as a slide -->
<div class="slides">
<section data-background="#1B325F" class="inverse">
<h1 class="title">Feature Model Synthesis</h1>
<h3>Steven She</h3>
<p class="text-center">
Generative Software Development Lab
</p>
</section>
<section>
<section>
<h2>What is Variability in Software?</h2>
<p class="lead" style="font-size: 1em;">
Variability in a software system is its ability for a system to adapt and customize for a particular context.
</p>
<p class="text-right">—van Gurp et al., 2001</p>
<div style="background: white; display: inline-block; padding-top: 1em;">
<div style="display:inline-block; vertical-align: top; margin-left: 1.5em;">
<img src="figs/galaxy-s2-hd-lte.jpg" alt="" class="no-border" height="250">
</div>
<div style="display:inline-block; vertical-align: top; margin: 0 0 0 1.5em;">
<img src="figs/iphone-5.jpg" alt="" class="no-border" height="280">
</div>
<div style="display:inline-block; vertical-align: top;">
<img src="figs/bbq10.jpg" alt="" class="no-border" height="280">
</div>
</div>
</section>
<section>
<h2>Why Variability Modeling?</h2>
<p class="bigskip lead">Large software systems contain variability
scattered over <em>documentation</em>, <em>design</em> and <em>implementation</em>.</p>
<div style="display: inline-block; vertical-align: middle;">e.g.,</div>
<div style="display: inline-block; vertical-align: middle;"><img class="no-border" src="figs/freebsd.png"></div>
</section>
<section>
<h2>Documentation</h2>
<div class="prettify bigskip"> <p>STACK enables the stack(9) facility... <strong>stack(9) will also be compiled in automatically if DDB(4) is compiled into the kernel</strong>.</p>
</div>
<div class="fragment">
<h2>Source Code</h2>
<div class="prettify">
<pre><code>#ifdef DDB
#ifndef KDB
#error KDB must be enabled for DDB to work!
#endif
#endif
</code></pre>
</div>
</div>
</section>
<section>
<h2 class="medskip">Configuring FreeBSD</h2>
<pre class="bigskip"><code>options SCHED_ULE #ULE scheduler
options PREEMPTION #Enable kernel thread preemption
options INET #InterNETworking
options INET6 #IPv6 communications protocols</code></pre>
<ul>
<li>FreeBSD is configured by setting values to config options.</li>
<li>Features and dependencies are scattered over documentation and code.</li>
<li>Difficult to get an <strong class="alert">overview of the variability</strong>.</li>
</ul>
</section>
<section>
<h2>Variability Models</h2>
<img src="figs/xconfig.png" width="490" class="smallskip">
<p class="text-center">Explicit model of a system's variability.</p>
<p class="text-center">Benefits include <strong class="alert">Graphical Configurators</strong> and <br><strong class="alert">Automated Analysis</strong>.</p>
</section>
</section>
<section>
<section>
<h2>Feature Models</h2>
<img class="no-border" src="figs/pmfm.tex.svg" style="zoom: 1.5;">
<p class="text-center">
Feature models describe the common and variable characteristics of products in a product line.
</p>
<ul>
<li>First introduced by Kang et al.</li>
<li>Describe a set of <em>legal configurations</em>.</li>
</ul>
</section>
<section>
<h2>Feature Model Syntax</h2>
<img class="no-border" src="figs/pmfm.tex.svg" style="zoom: 1.5;">
$$\mathsf{powersave} \land \mathsf{acpi} \rightarrow \mathsf{cpu\_hotplug}$$
</section>
<section>
<h2>Configuration Semantics</h2>
<p class="lead" style="margin-bottom: -.5em;">Feature models describe a set of<br> <strong class="alert">legal configurations</strong>.</p>
<p style="display: inline-block; vertical-align: middle; font-size: 6em; font-weight: 200; letter-spacing: -.2em; margin-right: .1em; margin-top: -.1em;">[[</p>
<div style="display: inline-block; vertical-align: middle;">
<img src="figs/fd-1.tex.svg" class="no-border" style="zoom: 2;">
</div>
<p style="display: inline-block; vertical-align: middle; font-size: 6em; font-weight: 200; letter-spacing: -.2em; margin-right: .2em; margin-top: -.1em;">]]</p>
<div style="display: inline-block; vertical-align: middle; font-size: 2em;">
\[ \mapsto \]
</div>
<div style="display: inline-block; vertical-align: middle;">
<p style="display: inline-block; font-size: 5em; font-weight: 200;">{</p>
<p style="display: inline-block;">
{ OS, staging },<br>
{ OS, staging, net},<br>
{ OS, staging, net, dst}
</p>
<p style="display: inline-block; font-size: 5em; font-weight: 200;">}</p>
</div>
<ul style="margin-top: .25em;">
<li>Represented as a propositional formula, \(\varphi\).</li>
<li>Satisfying assignments are the legal configurations.</li>
</ul>
</section>
</section>
<section>
<section id="scenarios">
<h2>What is Feature Model Synthesis?</h2>
<p class="lead">
Feature model synthesis is the construction
and design of a feature model given <strong class="alert">a set of features</strong> and <strong class="alert">legal combinations of features</strong>.
</p>
<img class="no-border" src="figs/flow.tex.svg" style="zoom: 1.8;">
</section>
<section>
<h2 class="bigskip">Applicable Synthesis Scenarios</h2>
<ol class="large smallskip">
<li>Synthesis From Product Configurations</li>
<li>Tool-Assisted Reverse Engineering from Code</li>
<li>Feature Model Merge Operations</li>
</ol>
</section>
<section>
<h2>From Product Configurations</h2>
<div class="text-center">
<img class="no-border" src="figs/scenario-variants-example.tex.svg" style="zoom: 2;" alt="">
</div>
<ul class="bigskip">
<li>Input consists of variants describing a product line.</li>
<li>e.g., model variants, products developed by cloning code.</li>
<li>Variants are compared and Variation Points (VPs) identified.</li>
<li>VPs and VP configurations used as input for synthesis.</li>
</ul>
</section>
<section>
<h2>Tool-Assisted Reverse Engineering from Code</h2>
<div class="text-center">
<img class="no-border" src="figs/scenario-code-example.tex.svg" style="zoom: 2;" alt="">
</div>
<ul class="bigskip">
<li>Input consists of source code containing variability.</li>
<li>e.g., FreeBSD with #ifdef annotated code.</li>
<li>Static analysis of #ifdef statements identifies code fragments as VPs and dependencies between VPs.</li>
</ul>
</section>
<section>
<h2>Feature Model Operations</h2>
<div class="text-center">
<img class="no-border" src="figs/fm-ops-1.tex.svg" style="zoom: 1.5;" alt=""><br>
<img class="no-border" src="figs/fm-ops-2.tex.svg" style="zoom: 1.5;" alt="">
</div>
<ul class="bigskip">
<li>Input consists of feature models.</li>
<li>Feature models translated to a prop. formula by configuration semantics.</li>
<li>Operation applied to formula then used as input to synthesis.</li>
</ul>
</section>
<section data-background="#C3D6EB">
<h2>Requirements for FM Synthesis</h2>
<dl>
<dt>Input</dt>
<dd>Support input as either Configurations or Dependencies.</dd>
<dt>Sound and Complete</dt>
<dd>Derive an exact feature model describing the input.</dd>
<dt>Scalable</dt>
<dd>Support 10 to 1000's of features (e.g., Linux, FreeBSD).</dd>
<dt>Hierarchy Selection</dt>
<dd>Use user input or heuristics to select a distinct feature hierarchy.</dd>
</dl>
</section>
</section>
<section>
<section data-background="#DFEEDB">
<h2 class="bigskip">Thesis Statement</h2>
<p class="lead">We efficiently synthesize <strong>large scale feature models</strong><br> with algorithms that use<br><em>SAT-based reasoning on propositional formulas</em> and<br>
that suggest a <strong>feature hierarchy</strong> with<br> <em>textual similarity heuristics</em>.
</p>
</section>
<section id="publications">
<h2>Contributions</h2>
<ol class="publications">
<li><strong class="alert">Feature Graph Extraction</strong>
<ul>
<li><strong class="alert">She</strong>, Ryssel, Andersen, Wasowski, Czarnecki, “Efficient
synthesis of feature models,” submitted for review in Journal of Information and Software Technology, 2013.</li>
<li><strong class="alert">She</strong>, Czarnecki, and Wasowski, “Usage scenarios for feature model synthesis,” in VARY Workshop, 2012.</li>
<li>
Andersen, Czarnecki, <strong class="alert">She</strong>, Wasowski, “Efficient synthesis of feature models,” in SPLC, 2012.
</li>
</ul>
</li>
</ol>
</section>
<section>
<h2>Contributions (cont.)</h2>
<ol class="publications" start="2">
<li><strong class="alert">Feature Tree Synthesis</strong>
<ul>
<li><strong class="alert">She</strong>, Lotufo, Berger, Wąsowski, Czarnecki, “Reverse engineering feature models,” in ICSE, 2011.</li>
</ul>
</li>
<li><strong class="alert">Kconfig & the Linux Variability Model</strong>
<ul>
<li><strong class="alert">She</strong>, Lotufo, Berger, Wąsowski, Czarnecki. “The variability model of the linux kernel,” in VaMoS Workshop, 2010.</li>
<li>Berger, <strong class="alert">She</strong>, Lotufo, Wasowski, Czarnecki, “Variability modeling in the real: a perspective from the operating systems domain,” in ASE, 2010.
</li>
<li>Berger, <strong class="alert">She</strong>, Lotufo, Wąsowski, Czarnecki. “A Study of Variability Models and Languages in the Systems Software Domain,” accepted in Transaction of Software Engineering, 2013.</li>
</ul>
</li>
</ol>
</section>
<section>
<h2>How the Algorithms Relate</h2>
<img src="figs/fge-fts.tex.svg" style="zoom: 2;" class="no-border">
</section>
</section>
<section>
<section id="fge" data-background="#1B325F" class="inverse">
<h1 class="title">Feature Graph Extraction</h1>
</section>
<section data-background="#C3D6EB">
<h2>Requirements for FM Synthesis</h2>
<dl>
<dt>Input</dt>
<dd>Support input as either Configurations or Dependencies.</dd>
<dt><strong class="alert">Sound and Complete</strong></dt>
<dd>Derive an exact feature model describing the input.</dd>
<dt>Scalable</dt>
<dd>Support 10 to 1000's of features (e.g., Linux, FreeBSD).</dd>
<dt>Hierarchy Selection</dt>
<dd>Use user input or heuristics to select a distinct feature hierarchy.</dd>
</dl>
</section>
<section>
<h2>Soundness and Completeness</h2>
<div style="margin-top: -30px;">
<p style="display: inline-block; font-size: 5em; font-weight: 200;">{</p>
<p style="display: inline-block;">
{ OS, staging },<br>
{ OS, staging, net},<br>
{ OS, staging, net, dst}
</p>
<p style="display: inline-block; font-size: 5em; font-weight: 200;">}</p>
</div>
<div class="clearfix"></div>
<div style="float: left; width: 32%; height: 330px; text-align: center;">
<img src="figs/fd-less.tex.svg" class="no-border" style="zoom: 2;">
<div class="caption">Less configs (sound)</div>
</div>
<div style="float: left; width: 33%; margin-right: .5%; height: 330px; text-align: center;">
<img src="figs/fd-more.tex.svg" class="no-border" style="zoom: 2;">
<div class="caption">More configs (complete)</div>
</div>
<div style="float: left; width: 32%; height: 330px; text-align: center;">
<img src="figs/fd-arbitrary.tex.svg" class="no-border" style="zoom: 2;">
<div class="caption" style="width: 32%;">Arbitrary</div>
</div>
</section>
<section>
<h2>Sound and Complete Synthesis</h2>
<div style="margin-top: -30px;">
<p style="display: inline-block; font-size: 5em; font-weight: 200;">{</p>
<p style="display: inline-block;">
{ OS, staging },<br>
{ OS, staging, net},<br>
{ OS, staging, net, dst}
</p>
<p style="display: inline-block; font-size: 5em; font-weight: 200;">}</p>
</div>
<div style="display: inline-block; width: 40%; margin-right: .5%; height: 300px; text-align: center; vertical-align: top;">
<img src="figs/fd-more.tex.svg" class="no-border" style="zoom: 2;">
<div class="caption" style="width: 40%;">Complete FD</div>
</div>
<div style="display: inline-block; width: 40%; margin-right: .5%; height: 300px; text-align: center; vertical-align: top;">
<img src="figs/fd-more.tex.svg" class="no-border" style="zoom: 2;">
\[
\mathsf{dst} \rightarrow \mathsf{net} \\
\]
<div class="caption" style="width: 40%;">Sound and Complete FD</div>
</div>
</section>
<!-- <section>
<div class="medskip">
Feature Models consists of a <em>Feature Diagram</em><br>and a <em>Cross-Tree Formula</em>.
</div>
<div class="medskip">
Feature Diagrams can't represent some inputs, e.g.
</div>
<div class="medskip large">
\[\begin{aligned}
\mathsf{bluetooth} \land \mathsf{wifi} &\rightarrow \mathsf{wireless}
\end{aligned}\]
</div>
<p>We synthesize a <strong>maximal, complete feature diagram</strong>. Any constraints not in the diagram form the cross-tree formula.</p>
</section>
-->
<section>
<h2>Maximal Feature Diagram</h2>
<div style="margin-top: -30px;">
<p style="display: inline-block; font-size: 5em; font-weight: 200;">{</p>
<p style="display: inline-block;">
{ OS, staging },<br>
{ OS, staging, net},<br>
{ OS, staging, net, dst}
</p>
<p style="display: inline-block; font-size: 5em; font-weight: 200;">}</p>
</div>
<div style="display:inline-block; height: 300px; text-align: center; width: 40%; vertical-align: top;">
<img src="figs/fd-more.tex.svg" class="no-border" style="zoom: 2;">
\[
\mathsf{dst} \rightarrow \mathsf{net} \\
\]
<div class="caption" style="width: 40%;">Non-maximal FD</div>
</div>
<div style="display: inline-block; height: 300px; text-align: center; vertical-align: top; width: 40%;">
<img src="figs/fd-2.tex.svg" class="no-border" style="zoom: 2;"><br>
<div class="caption" style="width: 40%;">Maximal FD</div>
</div>
</section>
<section>
<h2>Same Configs, Diff. Hierarchies</h2>
<div style="margin-top: -30px;">
<p style="display: inline-block; font-size: 5em; font-weight: 200;">{</p>
<p style="display: inline-block;">
{ OS, staging },<br>
{ OS, staging, net},<br>
{ OS, staging, net, dst}
</p>
<p style="display: inline-block; font-size: 5em; font-weight: 200;">}</p>
</div>
<div style="display: inline-block; height: 300px; text-align: center; vertical-align: top; width: 32%;">
<img src="figs/fd-1.tex.svg" class="no-border" style="zoom: 2;">
<div class="caption" style="width:32%;">FD<sub>1</sub></div>
</div>
<div style="display: inline-block; height: 300px; text-align: center; vertical-align: top; width: 32%;">
<img src="figs/fd-2.tex.svg" class="no-border" style="zoom: 2;">
<div class="caption" style="width:32%;">FD<sub>2<w/sub></div>
</div>
<div style="display: inline-block; height: 300px; text-align: center; vertical-align: top; width: 32%;">
<img src="figs/fd-3.tex.svg" class="no-border" style="zoom: 2;">
<div class="caption" style="width:32%;">FD<sub>3</sub></div>
</div>
</section>
<section>
<h2>Feature Graph</h2>
<div style="margin-top: -30px;">
<p style="display: inline-block; font-size: 5em; font-weight: 200;">{</p>
<p style="display: inline-block;">
{ OS, staging },<br>
{ OS, staging, net},<br>
{ OS, staging, net, dst}
</p>
<p style="display: inline-block; font-size: 5em; font-weight: 200;">}</p>
</div>
<div class="medskip"></div>
<div style="float: left; width: 300px; margin-right: 20px;">
<img src="figs/fg.tex.svg" class="no-border" style="zoom: 2.5;">
</div>
<ul style="float: left; width: 600px; margin-top: 30px;">
<li>Encapsulates <strong class="alert">all feature diagrams</strong> that are complete.</li>
<li>DAG as hierarchy, and overlapping feature groups.</li>
</ul>
<div class="clearfix"></div>
</section>
<section data-background="#C3D6EB">
<h2>Requirements for FM Synthesis</h2>
<dl>
<dt><strong class="alert">Input</strong></dt>
<dd>Support input as either Configurations or Dependencies.</dd>
<dt>Sound and Complete</dt>
<dd>Derive an exact feature model describing the input.</dd>
<dt>Scalable</dt>
<dd>Support 10 to 1000's of features (e.g., Linux, FreeBSD).</dd>
<dt>Hierarchy Selection</dt>
<dd>Use user input or heuristics to select a distinct feature hierarchy.</dd>
</dl>
</section>
<section>
<h3>Input as Configuration</h3>
<div style="margin-top: -30px; display: inline-block; vertical-align: middle;">
<p style="display: inline-block; font-size: 4em; font-weight: 200;">{</p>
<p style="display: inline-block; font-size: .8em;">
{ OS, staging },<br>
{ OS, staging, net},<br>
{ OS, staging, net, dst}
</p>
<p style="display: inline-block; font-size: 4em; font-weight: 200;">}</p>
</div>
<div style="display: inline-block; vertical-align: middle; font-size: 1.5em;">
\( \mapsto \)
</div>
<div style="display: inline-block; position: relative; width: 400px; vertical-align: middle; font-size: .7em;">\[
\begin{aligned}
&(\mathsf{OS} \land \mathsf{staging} \land \lnot \mathsf{net} \land \lnot\mathsf{dst}) \lor \\
&(\mathsf{OS} \land \mathsf{staging} \land \mathsf{net} \land \lnot\mathsf{dst}) \lor \\
&(\mathsf{OS} \land \mathsf{staging} \land \mathsf{net} \land \mathsf{dst})
\end{aligned}
\]
</div>
<div class="smallskip"></div>
<p class="text-center small">Configurations represented as DNF formula.</p>
<div class="fragment">
<div class="medskip"></div>
<!-- <p class="lead"><strong class="alert">A set of configurations</strong> represented as a DNF formula.</p> -->
<h3>Input as Dependencies</h3>
<p style="display: inline-block; font-size: 4em; font-weight: 200; vertical-align: middle;">{</p>
<div style="display: inline-block; vertical-align: middle; font-size: .7em;">\[
\begin{aligned}
\mathsf{staging} \lor \mathsf{net} &\rightarrow \mathsf{OS} \\
\mathsf{dst} &\rightarrow \mathsf{net} \\
\mathsf{OS} &\rightarrow \mathsf{staging}
\end{aligned}
\]</div>
<p style="display: inline-block; font-size: 4em; font-weight: 200; vertical-align: middle;">}</p>
<div style="display: inline-block; vertical-align: middle; font-size: 1.5em;">
\( \mapsto \)
</div>
<div style="display: inline-block; vertical-align: middle; font-size: .7em;">\[
\begin{aligned}
&(\lnot\mathsf{staging} \lor \mathsf{OS}) \land (\lnot\mathsf{net} \lor \mathsf{OS}) \land \\
&(\lnot \mathsf{dst} \lor \mathsf{net}) \land \\
&(\lnot\mathsf{OS} \lor \mathsf{staging})
\end{aligned}
\]</div>
<div class="smallskip"></div>
<p class="text-center small">Dependencies represented as a CNF Formula.</p>
</div>
</section>
<!-- <section data-background="#C3D6EB">
<h2>Requirements for FM Synthesis</h2>
<dl>
<dt><strong class="alert">Input</strong></dt>
<dd>Support input as either Configurations or Dependencies.</dd>
<dt><strong class="alert">Sound and Complete</strong></dt>
<dd>Derive an exact feature model describing the input.</dd>
<dt>Scalable</dt>
<dd>Support 10 to 1000's of features (e.g., Linux, FreeBSD).</dd>
<dt>Hierarchy Selection</dt>
<dd>Use user input or heuristics to select a distinct feature hierarchy.</dd>
</dl>
</section>
-->
<section>
<h2>Feature Graph Extraction (Fge)</h2>
<div style="display: inline-block; vertical-align: middle; margin-top: -30px;">
<p style="display: inline-block; vertical-align: middle; font-size: 2.5em;"><span data-fragment-index="2" class="fragment">FGE(</span><span>\(\varphi_{ \tiny \mathrm{CNF}, \mathrm{DNF} } \)</span><span class="fragment" data-fragment-index="2">)</span></p>
<div style="display: inline-block; vertical-align: middle; font-size: 2em" class="fragment" data-fragment-index="2">
\(\mapsto\)</div>
<div style="display: inline-block; vertical-align: middle;" class="fragment" data-fragment-index="2">
<img src="figs/fg.tex.svg" class="no-border" style="zoom: 2;">
</div>
<div class="fragment smallskip" data-fragment-index="3">
<img src="figs/flow-late.tex.svg" alt="" style="zoom: 1.5;" class="no-border">
</div>
<ul class="fragment" data-fragment-index="3">
<li><strong class="alert">Fully automatic</strong> algorithm for extracting feature graphs.</li>
<li>Algorithm uses a SAT solver.</li>
</ul>
</section>
<!--
<section>
<h2>Two Crucial Steps</h2>
<img src="figs/flow-late.tex.svg" alt="" style="zoom: 1.5;" class="no-border">
<dl>
<dt>DAG Hierarchy Recovery</dt>
<dd>Recovers the hierarchy as an Implication Graph.</dd>
<dt>Group and CTC Recovery</dt>
<dd>Recovers feature groups and cross-tree constraints.</dd>
</dl>
</section>
-->
<section>
<h2 class="smallskip">DAG Hierarchy Recovery</h2>
<div style="display: inline-block; vertical-align: middle; margin-right: 1em;">
<div style="font-size: 2.0em;">\[ \mathrm{DAG}(\varphi) \]</div>
</div>
<div style="display: inline-block; vertical-align: middle; margin-right: 1em;">
<div style="font-size: 2em;">\[ \mapsto \]</div>
</div>
<div style="display: inline-block; vertical-align: middle;">
<img src="figs/ig.tex.svg" alt="" style="zoom: 1.8;" class="no-border"><br>
</div>
<div style="clear: both;" class="bigskip"></div>
<ul>
<li>Given a formula, \(\varphi\), build an <strong class="alert">Implication Graph</strong>.</li>
<li>Each edge \((u,v)\) is an implication such that \(\varphi \land u \rightarrow v\)</li>
<li>Describes all possible hierarchies as a DAG.</li>
</ul>
</section>
<section>
<h2 class="medskip">Group and CTC Recovery</h2>
<dl>
<dt>Mutex Groups \([0..1]\)</dt>
<dd>Find <strong class="alert">maximal cliques</strong> in the <strong class="alert">mutex graph</strong> where an edge \((u,v)\) exists if \( \varphi \land u \rightarrow \lnot v \).</dd>
<dt>Or Groups \([1..n]\)</dt>
<dd>Given a parent \(p\), find <strong class="alert">prime implicates</strong> of \(\varphi \land p\) with the form \(f_1 \lor f_2 \lor \ldots \lor f_k \).
<br>
</dd>
<dt>Xor Groups \([1..1]\)</dt>
<dd>Groups that are both Mutex and Or groups.</dd>
</dl>
</section>
<section data-background="#C3D6EB">
<h2>Requirements for FM Synthesis</h2>
<dl>
<dt>Input</dt>
<dd>Support input as either Configurations or Dependencies.</dd>
<dt>Sound and Complete</dt>
<dd>Derive an exact feature model describing the input.</dd>
<dt><strong class="alert">Scalable</strong></dt>
<dd>Support 10 to 1000's of features (e.g., Linux, FreeBSD).</dd>
<dt>Hierarchy Selection</dt>
<dd>Use user input or heuristics to select a distinct feature hierarchy.</dd>
</dl>
</section>
<section>
<h2>Experimental Evaluation</h2>
<dl>
<dt>Purpose</dt>
<dd>Evaluate <strong class="alert">performance</strong> of our algorithms by comparing to other algorithms that build a feature graph.</dd>
<dt>Dataset</dt>
<dd><strong class="alert">Input representative of synthesis scenarios</strong>.<br>Derive input from FMs in a FM repository, generated FMs, and the Linux variability model.
</dd>
<dt>Measure</dt>
<dd><strong class="alert">Time</strong> needed to compute each part of a feature graph.<br>Quality does not need to evaluated.<br>Feature graph encapsulates all complete feature diagrams.</dd>
</dl>
<!-- <ul class="smallskip">
<li>Feature Model Synthesis is a <strong class="alert">NP-Hard problem</strong>.</li>
<li>Evaluate our algorithms against <strong class="alert">input representative of real world synthesis scenarios</strong>.</li>
<li>Compared Fge-CNF and Fge-DNF against two baseline algorithms with same inputs and outputs.</li>
<li>Measured <strong class="alert">computation time</strong> across the different steps of Feature Graph Extraction.</li>
</ul>
--> </section>
<section>
<h2>Evaluation Algorithms</h2>
<h3>Fge-CNF Evaluation</h3>
<table style="margin: auto;">
<thead>
<tr>
<td></td>
<td><strong>Fge-CNF</strong></td>
<td><strong>BDD-Based</strong> [Czarnecki and Wąsowski]</td>
</tr>
</thead>
<tr>
<td class="text-right"><strong>Input</strong></td>
<td>Dependencies</td>
<td>Dependencies</td>
</tr>
<tr>
<td class="text-right"><strong>Technique</strong></td>
<td>SAT Solver</td>
<td>Binary Decision Diagrams (BDDs)</td>
</tr>
</table>
<div class="bigskip"></div>
<div class="fragment">
<h3>Fge-DNF Evaluation</h3>
<table style="margin: auto;">
<thead>
<tr>
<td></td>
<td><strong>Fge-DNF</strong></td>
<td><strong>FCA-Based</strong> [Ryssel et al.]</td>
</tr>
</thead>
<tr>
<td class="text-right"><strong>Input</strong></td>
<td>Configurations</td>
<td>Configurations</td>
</tr>
<tr>
<td class="text-right"><strong>Technique</strong></td>
<td>SAT</td>
<td>Formal Concept Analysis and<br>Set Cover</td>
</tr>
</table>
</div>
</section>
<section>
<h2 class="smallskip">Dataset Characteristics</h2>
<div class="columns2">
<div class="column">
<h4 class="text-left">SPLOT Model Repository</h4>
<ul class="small">
<li>Largest, public repository of feature models.</li>
<li>267 FMs gathered from academic papers, experience reports, by volunteers.</li>
</ul>
</div>
<div class="column">
<h4 class="text-left">Generated Models</h4>
<ul class="small smallskip">
<li>20 generated FMs with difficult cross-tree constraints.</li>
</ul>
<h4 class="text-left">Linux Variability Model</h4>
<ul class="small" style="width: 100%;">
<li>5426 features.</li>
</ul>
</div>
</div>
<img src="figs/splot-size.svg" alt="" style="zoom: 1.3; padding: .25em; background: white;">
</section>
<section>
<h2 class="bigskip">Experiment Setup</h2>
<dl>
<dt>Null Hypothesis</dt>
<dd>
For each component of Fge, (i.e., implication graph, mutex graph, OR-groups) <strong class="alert">there is no difference in the mean computation times</strong> for Fge-CNF and Fge-BDD.
</dd>
</dl>
</section>
<section>
<h2>Fge-CNF vs. Fge-BDD Results</h2>
<h4>SPLOT Dataset</h4>
<table class="smallskip" style="margin: auto;">
<thead>
<tr>
<td>Component</td>
<td>Mean Difference (ms)</td>
<td class="text-right">p-value</td>
</tr>
</thead>
<tbody>
<tr>
<td>Implications</td>
<td class="text-right">-16</td>
<td class="text-right">0.63</td>
</tr>
<tr>
<td>Mutual Exclusions</td>
<td class="text-right">-20</td>
<td class="text-right">0.38</td>
</tr>
<tr>
<td>Or Groups</td>
<td class="text-right">-10,854</td>
<td class="text-right">1.13 x 10<sup>-9</sup></td>
</tr>
</tbody>
</table>
<p class="small text-center">Fge-CNF is <strong class="alert">significantly faster</strong> than the BDD-based algorithm for computing OR-Groups on the SPLOT dataset.</p>
<div class="columns2 fragment">
<div class="column">
<h4>Linux</h4>
<p class="small text-center">Fge-CNF completed in 7 hours.<br>The BDD-based algorithm <strong class="alert" style="white-space: nowrap;">ran out of memory</strong>.</p>
</div>
<div class="column">
<h4>Generated Dataset</h4>
<p class="small text-center">Fge-CNF completed 12 models.<br>The BDD-based algorithm <strong class="alert" style="white-space: nowrap;">timed out on all models</strong>.</p>
</div>
</div>
</dl>
</section>
<section>
<h2>Fge-DNF vs. FCA-Based Results</h2>
<h4>SPLOT Dataset</h4>
<table class="smallskip" style="margin: auto;">
<thead>
<tr>
<td>Component</td>
<td>Mean Difference (ms)</td>
<td>p-value</td>
</tr>
</thead>
<tbody>
<tr>
<td>Implications</td>
<td class="text-right">320</td>
<td class="text-right">0.0059</td>
</tr>
<tr>
<td>Mutual Exclusions</td>
<td class="text-right">166</td>
<td class="text-right">0.0012</td>
</tr>
<tr>
<td>Or Groups</td>
<td class="text-right">-3,904</td>
<td class="text-right">0.1214</td>
</tr>
</tbody>
</table>
<p class="small text-center">Performance of Fge-DNF is similar to that of the FCA-based algorithm, <strong class="alert">except for 5 models</strong> where Fge-DNF was significantly faster.</p>
</section>
<section>
<h2>Fge-DNF vs. FCA-Based (cont.)</h2>
<img src="figs/long-dnf-2.svg" style="zoom: 1.5; padding: .2em; background: white;">
<p class="text-center">Models had a large number of sibling features at the root.<br>Large search space for groups for FCA-based algorithm.</p>
</section>
<section>
<h2 class="medskip">Feature Graph Extraction Summary</h2>
<div style="display: inline-block; vertical-align: middle; margin-top: -30px;">
<p style="display: inline-block; vertical-align: middle; font-size: 2.5em;"><span>FGE(</span><span>\(\varphi_{ \tiny \mathrm{CNF}, \mathrm{DNF} } \)</span><span>)</span></p>
</div>
<div style="display: inline-block; vertical-align: middle; font-size: 2em">
\(\mapsto\)</div>
<div style="display: inline-block; vertical-align: middle;">
<img src="figs/fg.tex.svg" class="no-border" style="zoom: 2;">
</div>
<div class="smallskip"></div>
<ul>
<li>Fully automated algorithm.</li>
<li>Feature graph describes <strong class="alert">all possible feature diagrams</strong> that are complete for a given input.</li>
</ul>
</section>
</section>
<section>
<section id="fts" data-background="#1B325F" class="inverse">
<h1 class="title">Feature Tree Synthesis</h1>
</section>
<section>
<h2>How the Algorithms Relate</h2>
<div>
<img src="figs/fge-fts.tex.svg" style="zoom: 2;" class="no-border">
</div>
</section>
<section data-background="#C3D6EB">
<h2>Requirements for FM Synthesis</h2>
<dl>
<dt>Input</dt>
<dd>Support input as either Configurations or Dependencies.</dd>
<dt>Sound and Complete</dt>
<dd>Derive an exact feature model describing the input.</dd>
<dt>Scalable</dt>
<dd>Support 10 to 1000's of features (e.g., Linux, FreeBSD).</dd>
<dt><strong class="alert">Hierarchy Selection</strong></dt>
<dd>Use user input or heuristics to select a distinct feature hierarchy.</dd>
</dl>
</section>
<section>
<h2>Selecting a Hierarchy</h2>
<div class="columns2" style="position: relative;">
<div style="padding-top: .5em; display: inline-block; vertical-align: middle;width: 40%;">
<img src="figs/fg.tex.svg" class="no-border" style="zoom: 2;">
<div class="caption" style="width: 40%;">Feature Graph</div>
</div>
<div class="column" style="width: 25%;"><img src="figs/fd-2.tex.svg" alt="" class="no-border" style="zoom: 1.8;">
<div class="caption" style="width: 25%;">Feature Diagram <sub>1</sub></div>
</div>
<div class="column" style="width: 25%;"><img src="figs/fd-1.tex.svg" alt="" class="no-border" style="zoom: 1.8;">
<div class="caption" style="width: 25%;">Feature Diagram <sub>2</sub></div>
</div>
</div>
<div class="bigskip"></div>
<p class="text-center smallskip">How do we select a hierarchy out of all possible hierarchies?</p>
<p class="text-center alert">Feature Tree Synthesis combines logical constraints<br> with a textual similarity heuristic.</p>
</section>
<section>
<h2 class="bigskip">Two Lists of Potential Parents</h2>
<div class="medskip" style="float: left; margin-right: 20px; height: 400px;">
<img src="figs/mockup.svg" class="no-border" style="zoom: 1.3; vertical-align: middle;">
</div>
<dl class="small">
<dt>Ranked <strong>Implied Features</strong> (RIFs)</dt>
<dd>The implied features <strong class="alert">ranked by similarity</strong> to the selected feature.</dd>
<dt>Ranked <strong>All Features</strong> (RAFs)</dt>
<dd>All features in the input <strong class="alert">ranked by similarity</strong>. Handles incomplete input.</dd>
</dl>
</section>
<section>
<h2 class="medskip">Feature Similarity Measure Example</h2>
<p class="text-center">
Selecting a parent for:
</p>
<dl class="inline">
<dt>bluetooth</dt>
<dd>a <strong class="alert">network driver</strong>.</dd>
</dl>
<div class="bigskip"></div>
<dl class="inline small" style="display: inline-block; width: 600px; vertical-align: top;">
<dt>os_kernel</dt>
<dd>Operating systems</dd>
<dt>scheduler</dt>
<dd>I/O scheduling</dd>
<dt><strong class="alert">networking</strong></dt>
<dd><strong class="alert">Network</strong> <strong class="alert">drivers</strong></dd>
<dt>ethernet</dt>
<dd><div>Type of local area<br> <strong class="alert">networking</strong></div></dd>
</dl>
<div class="fragment" style="display: inline-block; width: 300px; vertical-align: top;">
<dl class"small">
<dt class="small">1. networking</dt>
<dt class="small">2. ethernet</dt>
<dt class="small">3. os_kernel</dt>