Towards More Relational Feature Models

Arnaud Gotlieb, Dusica Marijan and Sagar Sen

Certus Software V&V Center, Simula Research Laboratory, Lysaker, Norway

Keywords:

Feature Modeling, Variability, Constraint Programming.

Abstract:

Feature modeling is of paramount importance to capture variabilities and commonalities within a software

product line. Nevertheless, current feature modeling notations are limited, representing only propositional for-

mulae over attributed variables. This position paper advocates the extension of feature modeling formalisms

with richer computational domains and relational operations. In particular, it proposes to extend feature mod-

eling with ﬁnite and continuous domain variables, with ﬁrst-order logic quantiﬁers (∀,∃), and with N-ary

relations between features attributes, and with so-called global constraints. In order to extend the expres-

siveness while preserving automated analysis facilities, feature models could be semantically interpreted as

ﬁrst-order logic formulae (instead of propositional logic formulae), including global and continuous depen-

dency between features. In simpler words, this paper emphasizes the importance of having more relational

feature models and presents next-generation applications.

1 INTRODUCTION

This paper addresses the challenges imposed on Soft-

ware Product Line (SPL) engineering (Birk et al.,

2003)(Pohl et al., 2005) when engineers have to deal

with heterogeneous concerns about modeling, expres-

siveness, documentation and automation. Roughly

speaking, software engineers face a dual challenge:

increase the expressiveness of feature modeling no-

tations to deal with the complexity of product repre-

sentations, while keeping a high degree of automation

in the processing of their models. To illustrate this

dilemma, consider the following scenario:

The Product-line Engineer. Øystein works for a

Norwegian company, called ELB, producing highly-

conﬁgurable software control systems for automated

subsea oil&gas exploitation. He works as a product-

line engineer for ELB, meaning that he manages the

variability and commonalities of several similar prod-

ucts for various customers. To facilitate the commu-

nication with customers and product managers, Øys-

tein maintains a feature model (FM) representing all

the conﬁgurations of ELB control systems.

The Customer. Following a productive meeting

with Magne, a new customer of ELB working for a fa-

mous shipyard company, Øystein has tried to conﬁg-

ure a new variant of the product line. However, dur-

ing this process, he realized that Magne asked him to

consider an intricate situation: if the control system

embeds feature A, and if A is in mode 1, then feature

B needs to be excluded from the ﬁnal product, while if

A is in mode 2, then feature C needs to be excluded!

This is problematic for Øystein as features in FM can

only be represented as binary-state variables; the no-

tion of multiple modes is not available for features.

Another request by Magne is to conﬁgure a product

with no more than 25 features among a set of 57 fea-

tures.

The Product Managers. Later on, Øystein talked

to Kjetil and Hoyvind, both product managers at ELB.

Kjetil said that including feature A in a product, what-

ever be its mode, will automatically exclude similar

mode for feature B or feature C. Hoyvind, meanwhile,

said that, in any case, a product having both features

B and C in the same mode is impossible to develop.

Øystein is now a bit confused on how to capture these

important pieces of information in his FM. In addi-

tion, Hoyvind mentioned that feature E, representing

the voltage at the bounds of a subcomponent of the

control system, continuously depends on feature D,

because this feature is linked to D through a physical

formula. Øystein has absolutely no idea on how to

capture this dependency.

Issues in FM Modeling. Now, Øystein has to

return a call to Magne, the customer, to explain the

impossibility of developing the requested variant, but

he is totally confused. He does not know what are

the remaining options for deriving a feasible variant

381

Gotlieb A., Marijan D. and Sen S..

Towards More Relational Feature Models.

DOI: 10.5220/0005553403810386

In Proceedings of the 10th International Conference on Software Engineering and Applications (ICSOFT-EA-2015), pages 381-386

ISBN: 978-989-758-114-4

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

of the software product line? Are the two distinct

modes of feature A responsible for this impossibility?

Is the continuous dependency in between D and E

the cause of the unrealisable variant? Of course,

due to limited expressiveness of FM in general, the

informations Øystein gathered during the discussions

cannot be encoded in the FM and then it is useless

to answer these questions. Magne, the customer,

starts to be irritated not having clear answers to his

requests. Moreover, Øystein is clueless about incor-

porating the second request of Magne that states that

only 25 features be chosen for a subset of 57 features.

As illustrated by the above scenario, feature mod-

eling is of paramount importance for software prod-

uct conﬁguration (or derivation), product-line knowl-

edge documentation, negotiation among several pro-

fessionals, product design optimization and so on. For

managing these tasks altogether, one of the challenges

in feature modeling is to come up with a formalism

having the appropriate degree of expressiveness. As

the current underlying semantics of FM is based on

propositional logic, several restrictions prevent its us-

age in many realistic contexts. Another important

point to notice is the tremendous importance of au-

tomated support analysis of FM. In our view, this is

a key element for a widespread adoption of feature

modeling.

In this position paper, we address these limita-

tions by proposing a couple of extensions that are

inspired from Constraint Programming (CP) (Rossi

et al., 2006). The CP paradigm has brought con-

straint expressiveness to a higher degree by gather-

ing notions from various domains, including Logic

Programming, Operational Research and Artiﬁcial In-

telligence. In CP, ﬁnite and continuous domains are

recognized as powerful computational domains, over-

coming limitations stemming from the usage of a

boolean domain. CP is also a convenient tool to ad-

dress complex mathematical and conﬁguration prob-

lems, as a large body of efﬁcient constraint solving

techniques is available. Using CP in the context of

product conﬁguration (Klein, 1996) or feature mod-

eling is not a new idea (Benavides et al., 2005). It

has been successfully applied to solve difﬁcult prod-

uct conﬁguration problems (Gelle and Weigel, 1996)

and also to automatically analyse SPLs (Liang, 2012;

Marijan et al., 2013). However, as already pointed out

by others (Hubaux et al., 2012), CP is not yet fully ex-

ploited in the context of feature modeling. This paper

advocates the extension of FM notations to facilitate

design and automated analysis. In particular, the pa-

per makes the following contributions:

- Several relational extensions of FMs are introduced.

We propose 1) ﬁnite domain and continuous domain

variable encoding of features, 2) usage of N-ary and

global constraints, 3) universal quantiﬁcation over a

feature to increase the expressive power of a FM.

These extensions confer a competitive advantage to

a FM for variability modeling in SPLs;

- Using CP to support the relational FM extensions

allows us to preserve the efﬁciency of automated FM

analyses. For each proposed extension, we carefully

discuss automated support and constraint solver us-

age. Note however that the paper does neither provide

any concrete syntax for the relational extensions nor

any speciﬁc recommendation for selecting constraint

solvers;

- Two next-generation applications of these relational

extensions are discussed, opening perspectives for a

wider adoption of FM.

The paper is organized as follows: Sec.2 recalls

the basic principle of a FM and its semantics. Sec.3

introduces and discusses several relational FM exten-

sions. Finally, Sec.4 presents two next-generation ap-

plications.

2 FEATURE MODELING

Feature Model (FM) is a convenient graphical no-

tation to represent variability in SPLs (Kang et al.,

1990) and highly-conﬁgurable software systems

(Czarnecki et al., 2005), (Eriksson M. and K., 2005).

It is used to capture: (i) conﬁgurable software pa-

rameters (a.k.a. features) and (ii) dependencies be-

tween the features. The underlying interpretation (or

semantics) of a FM is however based on propositional

logic (Batory, 2005): A Feature Model is a propo-

sitional formula over a set of features; A feature is

a boolean variable that represents a composition el-

ement or a conﬁguration parameter; A product (or

conﬁguration) is a total assignment of features from

a FM. A feature is present within a product or con-

ﬁguration iff its corresponding variable equals to 1 or

True; A valid product is an assignment which satis-

ﬁes the propositional formula of a FM; A constraint

is a relation between two or more features. We dis-

tinguish between two types of constraints: A hier-

archical constraint is a relation among a father fea-

ture and its children features based on the follow-

ing operators AND, OR, XOR, OPT, CARD. A cross-

tree constraint is a binary relation among a pair of

features based on the operators REQUIRES, MUTEX.

Fig.1 represents a FM for Video-Conference Soft-

ware (VCS) products, extracted from a real-world

case study (Marijan et al., 2013). The model spec-

iﬁes that VCS supports calls, which can be either

ICSOFT-EA2015-10thInternationalConferenceonSoftwareEngineeringandApplications

382

Figure 1: Excerpt of a feature model for a video conferenc-

ing software.

P2P or Multisite calls, i.e., either 3x1024x576 max,

3x720p30 max or 1080p30–720p60 max. Op-

tionally, VCS supports 720p60 or 1080p30 pre-

mium resolution, or both. Conﬁgurations with

3x720p30 max or 1080p30–720p60 max resolution

must have Premium resolution feature.

For the FM shown in Fig.1, the set of features

[VCS,Call, Multisite, 3x1024x576 max] is a valid

product, but [VCS,Call, Multisite, 3x720p30 max]

is invalid, because the constraint between

3x720p30 max and Premium resolution features

is not satisﬁed. Since its introduction in 1990 (Kang

et al., 1990), feature modeling has been adopted in

some industrial sectors, e.g., (Dordowsky and Hipp,

2009), and has been derived into several dialects

(Schobbens et al., 2007).

3 RELATIONAL FEATURE

MODELS

This section introduces several extensions to increase

expressiveness of FMs. Each subsection discusses the

Pros/Cons of a speciﬁc extension in terms of com-

plexity and/or degree of automation.

3.1 From Boolean to Finite Domains

In traditional FMs, a feature is associated with a two-

state variable: it can either be present or absent within

a product. This is an over-simplistic view of the re-

ality where features have various (but often discrete)

states. We propose that each feature is associated with

a ﬁnite set of possible values, called modes. These

modes can advantageously be encoded using a Fi-

nite Domain (FD) variable A, where A is associated

a domain of possible modes modes(A) = {d

, . . . , d

}

where d

≥ 0. Note that, in a product, a feature can

only be assigned to a single mode. For example, mode

of feature A is used in product P

, while mode d

of the same feature is used in product P

. Thus, cross-

tree constraints can be deﬁned over mode values, e.g.,

A > 1 Requires B ≤ 1 meaning that any mode strictly

grater than 1 for A implies either mode 1 for B or

mode 0, interpreted as absence of B. This usage of

FD encoding of features is not really new and has

been reported in the literature, especially when au-

tomated analysis on FM is required (Benavides et al.,

2010). As a concrete example, the Multisite feature

of Fig.1 can be associated with a FD variable, having

mode value 1 equal to 3x1024x576 max, mode value

2 equal to 3x720p30 max, and mode value 3 equal

to 1080p30–720p60 max. Using this representation,

both cross-tree constraints can easily be encoded as

Multisite > 1 Requires Premium resolution = 1. One

could object that FD encoding is already possible in

current purely boolean FM, using a Xor node. How-

ever, using a Xor-node for encoding subtrees with

tens of leafs is not efﬁcient and using a FD variable

can considerably simplify the semantical interpreta-

tion of FMs. Indeed, as the Xor operator is binary

in boolean logic, it is required for any pair of leafs.

Thus, the number of Xor grows quadratically with the

number of leafs in any boolean interpretation of FM.

On the contrary, using FD variables, a single domain

membership constraint is required in the semantical

interpretation, e.g., A ← Xor(A

, A

) ∧ Xor(A

, A

) ∧

Xor(A

, A

) is encoded as A ∈ 1 . . . 3.

3.2 Featuring Global Constraints

Cross-tree constraints in FMs include binary con-

straints: (A Requires B) and (A Mutex B). How-

ever, several extensions have already been proposed

such as ternary relations or N-ary relations (Uzun-

caova et al., 2010; Martin Fagereng Johansen and

Fleurey, 2011). For example, in SPLOT (Mendonc¸a

et al., 2009), cross-tree constraints come as ternary

relations over booleans. There is no formal break-

through to switch from ternary to N-ary relations in

boolean algebra. It means that formal reasoning is in-

dependent from the arity of the initial relations. In

fact, this extension comes for free when using an

underlying SAT-solver or CP-solver to reason over

FMs. Nevertheless, we propose to go further by us-

ing non-ﬁxed arity global constraints among ﬁnite do-

main variables. Since two decades, researchers of the

CP community have built a rich catalog of global con-

straints to express various and complex relations used

for different applications. The most recent version of

the catalog contains more than 350 global constraints

(Beldiceanu et al., 2007).

Additionally, most CP solvers are incremental,

meaning that adding a constraint provokes constraint

propagation, which is a process that pushes conﬁgu-

ration choices throughout the constraint system. If an

TowardsMoreRelationalFeatureModels

383

assignment is (partially) consistent, then other vari-

able domains can be shrunk, while if it is inconsis-

tent, a backtracking process removes it and undoes

all the deductions. Constraint propagation is partic-

ularly useful during interactive product conﬁguration

as it enables early failure detection and backtracking.

When conﬁguring a product, one can easily evaluate

the consequences of a conﬁguration choice for other

features. For example, including features F

, F

in a

product where Sum ctr([F

, F

], ≤, 2) is enforced,

automatically assigns 0 for F

3.3 Adding Logical Quantiﬁers

FMs are interpreted as propositional logic formu-

las: features cannot be quantiﬁed. Extending FMs

to ﬁrst-order logic formulas means that features can

be existentially and universally quantiﬁed. Basically,

this extension enables simple expression of complex

relations among feature modes. Feature universal

quantiﬁcation is interesting to express invariants over

SPLs and has already been drafted in the Clafer lan-

guage (Antkiewicz et al., 2013). For example, ex-

pressing that for each mode value of feature A, there

exists a mode value of feature B that satisﬁes a spe-

ciﬁc property P can easily be formulated as: ∀d ∈

modes(A), ∃t

∈ modes(B), such that P holds. Sup-

port for automatic reasoning over ﬁrst-order formulae

is crucial when enriching the semantics of FMs. Re-

cently, tools, called as QCSP-solvers, have been de-

veloped to support such reasoning in the context of

ﬁnite domain constraint solving (Gent et al., 2008). It

becomes possible to solve efﬁciently constraints such

as ∃x∀y(x 6= y) =⇒ ∃z(z < x) ∧ (z < y). For exam-

ple, QeCode is a QCSP-solver available online that

shows reasonable performances, provided that con-

straints stay simple. However, extending FM to high-

order logics, enabling quantiﬁcation over operations

among the features, would compromise the efﬁciency

of automated analyses.

3.4 Continuous Domains and

Dependencies

Using continuous variables in product conﬁguration is

well known (Xie et al., 2006). Even if discretization

of continuous variables is often possible (e.g., con-

sidering that a voltage takes a value in only N pos-

sibilities {v

, . . . , v

}), introducing continuous vari-

able increases the expressive power of a FM. Indeed,

very often, discrete values are not available at prod-

uct conﬁguration time because they depend on other

components, not yet available. In addition, physical

variables in systems are known with tolerance ranges,

coming from the speciﬁcations of electronic compo-

nents, that cannot be handled accurately with dis-

cretized values. Finally, conﬁguration variables may

only take values resulting from complex mathemat-

ical computations. As a consequence, these values

cannot be represented using pre-selected discrete val-

ues. For example, consider the relation y

− x ≤ 0

and the value 0.1 for x. The domain of y can only

be represented as a range of possible real values, i.e.,

[−0.01, 0.01]. Any discretization of this range would

inaccurately represent the relation. Most of the phys-

ical variables of a system are linked together with

continuous relations (e.g., Ohm law for electronic

components), but representing them with non-discrete

variables in FMs for SPL is questionable. One can ar-

gue that physical entities may not correspond to con-

ﬁgurable software parameters. We believe however

that introducing continuous variables for conﬁguring

a product could open FMs to a wider range of appli-

cations. As a simple example, consider the design of

a cylindrical vessel deﬁned by two continuous vari-

ables: height and radius. The volume of the ves-

sel could be maintained in a FM by the constraint

V = π × radius

× height. Even if height and radius

are sufﬁcient to conﬁgure the vessel and could thus be

discretized, a ﬁnal user may want to conﬁgure the ves-

sel through its volume instead of these two variables.

Usually, physical variables take their values in pre-

deﬁned ranges, for which it is interesting to estimate

the extreme values (e.g., what is the maximal vessel

volume that can be computed). So, capturing the con-

tinuous relation between these variables, that are re-

ﬂected in a FM by feature variables, is interesting for

conﬁguration purposes. This proposition would be

meaningless without the support of operational con-

straint solvers over continuous domains. Fortunately,

solvers such as Interlog (Lhomme et al., 1998), IBM

Ilog-Labs CP-Optimizer or RealPaver (Granvilliers,

2003) are available for that purpose. Note also that re-

cent developments in constraint solving over ﬂoating-

point computations have led to the design of speciﬁc

solvers that tackle correctly rounding modes and ap-

proximations (Bagnara et al., 2013). It could be cru-

cial for some safety-critical software product lines to

capture accurately relations over ﬂoating-point com-

putations, especially if the variability models are used

to select software components in order to integrate a

complete product release.

4 NEXT-GENERATION

APPLICATIONS

Extending feature modeling is interesting iff the evi-

ICSOFT-EA2015-10thInternationalConferenceonSoftwareEngineeringandApplications

384

dences of its beneﬁts can be shown in practice. For

instance, the scenario presented in the introduction is

realistic and corresponds to a situation addressed by

researchers of the Certus center. In this section, we

go a step further and present the application of rela-

tional feature models to some next-generation appli-

cation domains.

4.1 Context-aware Sensor Fusion

Raw data from sensors and user interaction come in

variable frequencies, from ﬁnite/continuous domains,

and have different domain types such as strings, re-

als, and integers. A fusion of the signals received at

an instant needs to be modelled and analyzed to accu-

rately deﬁne a context. For instance, in (Acher et al.,

2009), FMs are used to represent environmental con-

texts with features such as luminosity. A context con-

ﬁguration is mapped to the conﬁguration of a vision

system. The choice of RGB camera or infra-red cam-

era is based on detected luminosity, which is a vari-

able with a continuous domain. However, a FM is

severely limited by the boolean nature of feature vari-

ables, easily giving a rise to an exponentially growing

context FM. We believe that extending FMs with con-

tinuous domain variables could simplify the modeling

of sensor fusion applications.

4.2 Filtering in Big Data

The explosion of data from business processes, social

networks, and scientiﬁc instruments presents both the

boon of data and the bane of processing it. Often big

data contains numerous redundancies or even faulty

data due to measurement errors. Therefore, there is a

necessity to select data records in a controlled man-

ner. Relational FMs can be used to model a ﬁlter

for a large number of multivariate data records in a

database. Data records that are a valid conﬁguration

of a relational FM can be selected for further process-

ing. A relational FM can be seen as ﬁlter for selecting

correct and representative data records in Big Data. In

(Sen and Gotlieb, 2013), FMs are used to model vari-

ation in data-intensive systems: 160 currencies and

900 different types of taxes are modeled as features.

There are thousands of pairwise interactions between

these two sets of features. Representing such a large

variation of a data ﬁeld as a set of boolean features

in a graphical FM is highly unreadable. Therefore, a

paradigm shift in the standard for feature modelling is

needed.

5 CONCLUSIONS

Relational FMs are promising for opening new appli-

cations and research directions. For us, CP can drive

such extensions through FD and continuous domains

extensions, global constraints, and logical quantiﬁca-

tion, because they preserve automated analyses capa-

bilities over FMs.

ACKNOWLEDGEMENTS

This work is partially supported by the Research

Council of Norway (RCN) through the Research-

based Innovation Center (SFI Programme) Certus.

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