Skip to main content
SpringerLink
Log in

Finding suitable variability abstractions for lifted analysis

  • Original Article
  • Published:
Formal Aspects of Computing

Abstract

Many software systems are today variational: they are built as program families or Software Product Lines. They can produce a potentially huge number of related programs, known as products or variants, by selecting suitable configuration options (features) at compile time. Many such program families are safety critical, yet the appropriate tools only rarely are able to analyze them effeciently. Researchers have addressed this problem by designing specialized variability-aware static (dataflow) analyses, which allow analyzing all variants of the family, simultaneously, in a single run without generating any of the variants explicitly. They are also known as lifted or family-based analyses. They take as input the common code base, which encodes all variants of a program family, and produce precise analysis results corresponding to all variants. These analyses scale much better than “brute force” approach, where all individual variants are analyzed in isolation, one-by-one, using off-the-shelf single-program analyzers. Nevertheless, the computational cost of lifted analyses still greatly depends on the number of features and variants (which is often huge). For families with a large number of features and variants, the lifted analyses may be too costly or even infeasible. In order to speed up lifted analyses and make them computationally cheaper, variability abstractions which simplify variability away from program families and lifted analyses have been introduced. However, the space of possible variability abstractions is still intractably large to search naively, with most abstractions being either too imprecise or too costly.

We introduce here a method to efficiently find suitable variability abstractions from a large space of possible abstractions for a lifted static analysis. The main idea is to use a pre-analysis to estimate the impact of variability-specific parts of the program family on the analysis’s precision. The pre-analysis is fully variability-aware while it aggressively abstracts the other semantics aspects. Then we use the pre-analysis results to find out when and where the subsequent abstract lifted analysis should turn off or on its variability-awareness. The abstraction constructed in this way is effective in discarding variability-specific program details that are irrelevant for showing the analysis’s ultimate goal. We formalize this approach and we illustrate its effectiveness on several Java case studies. The evaluation shows that our approach which consists of running a pre-analysis followed by a subsequent abstract lifted analysis achieves competitive the precision-speed tradeoff compared to the standard lifted analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Apel, S., Kästner, C.: An overview of feature-oriented software development. J Object Technol 8(5), 49–84 (2009)

    Article  Google Scholar 

  2. Batory D (2005) Feature models, grammars, and propositional formulas. In: 9th International software product lines conference, SPLC '05, volume 3714 of LNCS, Springer-Verlag, pp 7–20

  3. Brabrand, C., Ribeiro, M., Tolêdo, T., Winther, J., Borba, P.: Intraprocedural dataflow analysis for software product lines. Trans Asp Oriented Softw Dev 10, 73–108 (2013)

    Article  Google Scholar 

  4. Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans Comput 35(8), 677–691 (1986)

    Article  MATH  Google Scholar 

  5. Bodden E, Tolêdo T, Ribeiro M, Brabrand C, Borba P, Mezini M (2013) \(\text{Spl}^{{{\rm lift}}}\): statically analyzing software product lines in minutes instead of years. In: ACM SIGPLAN conference on PLDI '13, pp 355–364

  6. Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Sethi, R. (ed.) POPL'77, pp. 238–252. Los Angeles, California (1977)

    Chapter  Google Scholar 

  7. Cousot P, Cousot R (1979) Systematic design of program analysis frameworks. In: POPL'79, pp 269–282

  8. Cousot, P., Cousot, R.: Abstract interpretation and application to logic programs. J Log Program 13(2–3), 103–179 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chen J, Cousot P (2015) A binary decision tree abstract domain functor. In: Static analysis—22nd international symposium, SAS 2015, Saint-Malo, France, September 9–11, 2015, Proceedings, volume 9291 of LNCS, Springer, pp 36–53

  10. Classen, A., Cordy, M., Heymans, P., Legay, A., Schobbens, P.-Y.: Model checking software product lines with SNIP. STTT 14(5), 589–612 (2012)

    Article  Google Scholar 

  11. Cousot P, Cousot R, Mauborgne L (2010) A scalable segmented decision tree abstract domain. In: Time for verification, essays in memory of Amir Pnueli, volume 6200 of LNCS, Springer, pp 72–95

  12. Classen, A., Cordy, M., Schobbens, P.-Y., Heymans, P., Legay, A., Raskin, J.-F.: Featured transition systems: Foundations for verifying variability-intensive systems and their application to LTL model checking. IEEE Trans Softw Eng 39(8), 1069–1089 (2013)

    Article  Google Scholar 

  13. Chrszon, P., Dubslaff, C., Klüppelholz, S., Baier, C.: Profeat: feature-oriented engineering for family-based probabilistic model checking. Formal Asp Comput 30(1), 45–75 (2018)

    Article  MathSciNet  Google Scholar 

  14. Chen S, Erwig M, Walkingshaw E (2012) An error-tolerant type system for variational lambda calculus. In: ACM SIGPLAN international conference on functional programming, ICFP'12, pp 29–40

  15. Classen A, Heymans P, Schobbens P-Y, Legay A (2011) Symbolic model checking of software product lines. In: Proceedings of the 33rd international conference on software engineering, ICSE 2011, pp 321–330

  16. Clements, P., Northrop, L.: Software product lines: practices and patterns. Addison-Wesley, Boston (2001)

    Google Scholar 

  17. Cousot, P.: The calculational design of a generic abstract interpreter. In: Broy, M., Steinbrüggen, R. (eds.) Calculational system design, NATO ASI series F, pp. 1–88. IOS Press, Amsterdam (1999)

    Google Scholar 

  18. Chechik M, Stavropoulou I, Disenfeld C, Rubin J (2018) FPH: efficient non-commutativity analysis of feature-based systems. In: Fundamental approaches to software engineering, 21st international conference, FASE 2018, proceedings., volume 10802 of LNCS, Springer, pp 319–336

  19. Cordy M, Schobbens P-Y, Heymans P, Legay A (2012) Behavioural modelling and verification of real-time software product lines. In: 16th International software product line conference, SPLC '12, Vol 1. ACM, pp 66–75

  20. Dimovski AS, Al-Sibahi AS, Brabrand C, Wasowski A (2015) Family-based model checking without a family-based model checker. In: Model checking software—22nd international symposium, SPIN 2015, proceedings, volume 9232 of LNCS, Springer, pp 282–299

  21. Dimovski, A., Al-Sibahi, A.S., Brabrand, C., Wasowski, A.: Efficient family-based model checking via variability abstractions. STTT 19(5), 585–603 (2017)

    Article  Google Scholar 

  22. Dimovski AS, Brabrand C, Wasowski A (2015) Variability abstractions: trading precision for speed in family-based analyses. In: 29th European conference on object-oriented programming, ECOOP 2015, volume 37 of LIPIcs, Schloss Dagstuhl—Leibniz-Zentrum fuer Informatik, pp 247–270

  23. Dimovski AS, Brabrand C, Wasowski A (2016) Finding suitable variability abstractions for family-based analysis. In: FM 2016: formal methods—21st international symposium, proceedings, volume 9995 of LNCS, pp 217–234

  24. Dimovski, A.S., Brabrand, C., Wasowski, A.: Variability abstractions for lifted analysis. Sci Comput Program 159, 1–27 (2018)

    Article  Google Scholar 

  25. Dimovski, A.: Program verification using symbolic game semantics. Theor Comput Sci 560, 364–379 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  26. Dimovski AS (2016) Symbolic game semantics for model checking program families. In: Model checking software—23nd international symposium, SPIN 2016, proceedings, volume 9641 of LNCS, Springer, pp 19–37

  27. Dimovski AS (2018) Abstract family-based model checking using modal featured transition systems: preservation of . In: Fundamental approaches to software engineering, 21st international conference, FASE 2018, proceedings., volume 10802 of LNCS, Springer, pp 301–318

  28. Dimovski, A.S.: Verifying annotated program families using symbolic game semantics. Theor Comput Sci 706, 35–53 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  29. Dimovski AS, Wasowski A (2017) From transition systems to variability models and from lifted model checking back to UPPAAL. In: Models, algorithms, logics and tools—essays dedicated to kim guldstrand Larsen on the occasion of his 60th birthday, volume 10460 of LNCS, Springer, pp 249–268

  30. Dimovski AS, Wasowski A (2017) Variability-specific abstraction refinement for family-based model checking. In: Fundamental approaches to software engineering—20th international conference, FASE 2017, proceedings, volume 10202 of LNCS, pp 406–423

  31. Erwig M, Walkingshaw E (2011) The choice calculus: a representation for software variation. ACM Trans Softw Eng Methodol 21(1):6:1–6:27

  32. Gazzillo P, Grimm R (2012) Superc: parsing all of C by taming the preprocessor. In: Vitek J, Lin H, Tip F (eds) ACM SIGPLAN conference on programming language design and implementation, PLDI '12, Beijing, China—June 11–16, 2012, ACM, pp 323–334

  33. Iosif-Lazar AF, Al-Sibahi AS, Dimovski AS, Savolainen JE, Sierszecki K, Wasowski A (2015) Experiences from designing and validating a software modernization transformation (E). In: 30th IEEE/ACM International conference on automated software engineering, ASE 2015, pp 597–607

  34. Iosif-Lazar, A.F., Melo, J., Dimovski, A.S., Brabrand, C., Wasowski, A.: Effective analysis of c programs by rewriting variability. Program J 1(1), 1 (2017)

    Article  Google Scholar 

  35. Jeannet B, Miné A (2009) Apron: a library of numerical abstract domains for static analysis. In: Computer aided verification, 21st international conference, CAV 2009. Proceedings, volume 5643 of LNCS, Springer, pp 661–667

  36. Christian K, Apel S (2008) Type-checking software product lines—a formal approach. In: 23rd IEEE/ACM international conference on automated software engineering (ASE) 2008), pp 258–267

  37. Kästner C, Apel S, Kuhlemann M (2008) Granularity in software product lines. In: Proceedings of the 30th international conference on software engineering (ICSE'08), Leipzig, Germany, ACM, pp 311–320

  38. Kastner C (2010) Virtual separation of concerns: toward preprocessors 2.0. Ph.D. thesis, University of Magdeburg, Germany

  39. Kästner C, Giarrusso PG, Rendel T, Erdweg S, Ostermann K, Berger T (2011) Variability-aware parsing in the presence of lexical macros and conditional compilation. In: Proceedings of the 26th annual ACM SIGPLAN conference on object-oriented programming, systems, languages, and applications, OOPSLA 2011, part of SPLASH 2011, pp 805–824

  40. Larsen KG, Nyman U, Wasowski A (2007) Modal I/O automata for interface and product line theories. In: Programming languages and systems, 16th European symposium on programming, ESOP 2007, proceedings, volume 4421 of LNCS, Springer, pp 64–79

  41. Liang P, Tripp O, Naik M (2011) Learning minimal abstractions. In: Proceedings of the 38th ACM SIGPLAN-SIGACT symposium on principles of programming languages, POPL 2011, pp 31–42

  42. Midtgaard, J., Dimovski, A.S., Brabrand, C., Wasowski, A.: Systematic derivation of correct variability-aware program analyses. Sci Comput Program 105, 145–170 (2015)

    Article  Google Scholar 

  43. Meinicke J, Wong C-P, Kästner C, Thüm T, Saake G (2016) On essential configuration complexity: measuring interactions in highly-configurable systems. In: Proceedings of the 31st IEEE/ACM international conference on automated software engineering, ASE 2016, Singapore, September 3–7, 2016, ACM, pp 483–494

  44. Nielson, F., Nielson, H.R., Hankin, C.: Principles of program analysis. Springer, Secaucus (1999)

    Book  MATH  Google Scholar 

  45. Naik M, Yang H, Castelnuovo G, Sagiv M (2012) Abstractions from tests. In: Proceedings of the 39th ACM SIGPLAN-SIGACT symposium on principles of programming languages, POPL 2012, pp 373–386

  46. Oh H, Lee W, Heo K, Yang H, Yi K (2014) Selective context-sensitivity guided by impact pre-analysis. In: ACM SIGPLAN conference on programming language design and implementation, PLDI '14, p 49

  47. Oh, H., Lee, W., Heo, K., Yang, H., Yi, K.: Selective x-sensitive analysis guided by impact pre-analysis. ACM Trans Program Lang Syst 38(2), 6 (2016)

    Google Scholar 

  48. Dalla Preda, M., Giacobazzi, R., Debray, S.K.: Unveiling metamorphism by abstract interpretation of code properties. Theor Comput Sci 577, 74–97 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  49. Reps T, Horwitz S, Sagiv M (1995) Precise interprocedural dataflow analysis via graph reachability. In: Proceedings of 22nd ACM SIGPLAN-SIGACT symposium on principles of programming languages, POPL '95, pp 49–61

  50. Rival, X., Mauborgne, L.: The trace partitioning abstract domain. ACM Trans Program Lang Syst 29(5), 26 (2007)

    Article  Google Scholar 

  51. Scholz W, Thüm T, Apel S, Lengauer C (2011) Automatic detection of feature interactions using the java modeling language: an experience report. In: Software product lines—15th international conference, SPLC 2011, workshop proceedings, Vol 2. ACM, p 7

  52. Thüm T, Apel S, Kästner C, Schaefer I, Saake G (2014) A classification and survey of analysis strategies for software product lines. ACM Comput Surv 47(1):6:1–6:45

  53. ter Beek, M.H., Fantechi, A., Gnesi, S., Mazzanti, F.: Modelling and analysing variability in product families: model checking of modal transition systems with variability constraints. J Log Algebr Methods Program 85(2), 287–315 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  54. Urban C, Miné A (2014) A decision tree abstract domain for proving conditional termination. In: Static analysis—21st international symposium, SAS 2014. Proceedings, volume 8723 of LNCS, Springer, pp 302–318

  55. von Rhein A (2016) Analysis strategies for configurable systems. Ph.D. thesis, University of Passau, Germany

  56. Vallée-Rai R, Co P, Gagnon E, Hendren L, Lam P, Sundaresan V (1999) Soot—a java bytecode optimization framework. In: Proceedings of the 1999 conference of the centre for advanced studies on collaborative research (CASCON'99), IBM Press, pp 13

  57. Winskel, G.: The formal semantics of programming languages. The MIT Press, Cambridge, Foundation of computing series (1993)

    MATH  Google Scholar 

  58. Zhang X, Naik M, Yang H (2013) Finding optimum abstractions in parametric dataflow analysis. In: ACM SIGPLAN conference on programming language design and implementation, PLDI '13, pp 365–376

Download references

Funding

Funding was provided by The Danish Council for Independent Research under a Sapere Aude project (Grant No. 0602-02327B).

Author information

Authors and Affiliations

  1. Mother Teresa University, 12 Udarna Brigada 2a, 1000, Skopje, Macedonia

    Aleksandar S. Dimovski

  2. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Claus Brabrand & Andrzej Wąsowski

Authors
  1. Aleksandar S. Dimovski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Claus Brabrand
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andrzej Wąsowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aleksandar S. Dimovski.

Additional information

Connie Heitmeyer, Ana Cavalcanti, John Fitzgerald, and Stefania Gnesi

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dimovski, A.S., Brabrand, C. & Wąsowski, A. Finding suitable variability abstractions for lifted analysis. Form Asp Comp 31, 231–259 (2019). https://doi.org/10.1007/s00165-019-00479-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00165-019-00479-y

Keywords

Search

Navigation