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Quantitative properties of featured automata

  • Foundations for Mastering Change
  • Quantitative Variability Modelling and Analysis
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Abstract

A featured transition system is a transition system in which the transitions are annotated with feature expressions: Boolean expressions on a finite number of given features. Depending on its feature expression, each individual transition can be enabled when some features are present, and disabled for other sets of features. The behavior of a featured transition system hence depends on a given set of features. There are algorithms for featured transition systems which can check their properties for all sets of features at once, for example for LTL or CTL properties. Here we introduce a model of featured weighted automata which combines featured transition systems and (semiring-) weighted automata. We show that methods and techniques from weighted automata extend to featured weighted automata and devise algorithms to compute quantitative properties of featured weighted automata for all sets of features at once. We show applications to minimum reachability and to energy properties.

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References

  1. Bloom, S. L.: Ésik, Z.: Iteration theories: the equational logic of iterative processes. EATCS Monographs on Theoretical Computer Science. Springer (1993)

  2. Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N.: Timed automata with observers under energy constraints. In: Johansson, K.H., Wang, Y. (eds.) HSCC, pp. 61–70. ACM (2010)

  3. Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N., Srba, J.: Infinite runs in weighted timed automata with energy constraints. In: Cassez, F., Claude, J. (eds.) Formats, volume 5215 of LNCS, pp. 33–47. Springer (2008)

  4. Bouyer, P., Larsen, K.G., Markey, N.: Lower-bound constrained runs in weighted timed automata. In: QEST, pp. 128–137. IEEE Computer Society (2012)

  5. Chatterjee, K., Doyen, L.: Energy parity games. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP (2), volume 6199 of LNCS, pp. 599–610. Springer (2010)

  6. 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 

  7. Conway, J.H.: Regular Algebra and Finite Machines. Chapman and Hall, London (1971)

    MATH  Google Scholar 

  8. Cordy, M., Schobbens, P.-Y., Heymans, P., Legay, A.: Behavioural modelling and verification of real-time software product lines. In: de Almeida, E.S., Schwanninger, C., Benavides, D. (eds.) SPLC, pp. 66–75. ACM (2012)

  9. Cordy, M., Schobbens, P.-Y., Heymans, P., Legay, A.: Beyond boolean product-line model checking: dealing with feature attributes and multi-features. In: Notkin, D., Cheng, B.H.C., Pohl, K. (eds.) ICSE, pp. 472–481. IEEE/ACM (2013)

  10. Degorre, A., Doyen, L., Gentilini, R., Raskin, J.-F., Torunczyk, S.: Energy and mean-payoff games with imperfect information. In: CSL, pp. 260–274 (2010)

    Chapter  Google Scholar 

  11. Droste, M., Kuich, W., Vogler, H.: Handbook of Weighted Automata. Springer, Berlin (2009)

    Book  Google Scholar 

  12. Droste, M., Meinecke, I.: Weighted automata and regular expressions over valuation monoids. Int. J. Found. Comput. Sci. 22(8), 1829–1844 (2011)

    Article  MathSciNet  Google Scholar 

  13. Ésik, Z., Fahrenberg, U., Legay, A.: \(^*\)-continuous Kleene \(\omega \)-algebras. In: Potapov, I. (ed) DLT, volume 9168 of LNCS, pp. 240–251. Springer (2015)

  14. Ésik, Z., Fahrenberg, U., Legay, A.: \(^*\)-continuous Kleene \(\omega \)-algebras for energy problems. In: Matthes, R., Mio, M. (eds.) FICS, volume 191 of EPTCS, pp. 48–59 (2015)

  15. Ésik, Z., Fahrenberg, U., Legay, A., Quaas, K.: Kleene algebras and semimodules for energy problems. In: Hung, D.V., Ogawa, M. (eds.) ATVA, volume 8172 of LNCS, pp. 102–117. Springer (2013)

  16. Ésik, Z., Fahrenberg, U., Legay, A., Quaas, K.: An algebraic approach to energy problems I: \({}^*\)-continuous Kleene \(\omega \)-algebras. Acta Cybern. 23(1), 203–228 (2017)

    Article  MathSciNet  Google Scholar 

  17. Ésik, Z., Fahrenberg, U., Legay, A., Quaas, K.: An algebraic approach to energy problems II: The algebra of energy functions. Acta Cybern. 23(1), 229–268 (2017)

    Article  MathSciNet  Google Scholar 

  18. Ésik, Z., Kuich, W.: On iteration semiring-semimodule pairs. Semigroup Forum 75, 129–159 (2007)

    Article  MathSciNet  Google Scholar 

  19. Ésik, Z., Kuich, W.: Finite automata. In: Handbook of Weighted Automata [11], pp. 69–104

    Google Scholar 

  20. Fahrenberg, U., Juhl, L., Larsen, K.G., Srba, J.: Energy games in multiweighted automata. In: ICTAC, volume 6916 of LNCS, pp. 95–115. Springer (2011)

  21. Fahrenberg, U., Legay, A.: Featured weighted automata. In: FormaliSE@ICSE, pp. 51–57. IEEE(2017)

  22. Kozen, D.: A completeness theorem for Kleene algebras and the algebra of regular events. Inf. Comput. 110(2), 366–390 (1994)

    Article  MathSciNet  Google Scholar 

  23. Olaechea, R., Fahrenberg, U., Atlee, J.M., Legay, A.: Long-term average cost in featured transition systems. In: Hong, M (ed) SPLC, pp. 109–118. ACM (2016)

  24. Quaas, K.: On the interval-bound problem for weighted timed automata. In: Dediu, A.-H., Inenaga, S., Martín-Vide, C. (eds.) LATA, volume 6638 of LNCS, pp. 452–464. Springer (2011)

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

    Article  Google Scholar 

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Authors and Affiliations

  1. École polytechnique, Palaiseau, France

    Uli Fahrenberg

  2. Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Axel Legay

  3. Aalborg University, Aalborg, Denmark

    Axel Legay

Authors
  1. Uli Fahrenberg
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  2. Axel Legay
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Correspondence to Uli Fahrenberg.

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Fahrenberg, U., Legay, A. Quantitative properties of featured automata. Int J Softw Tools Technol Transfer 21, 667–677 (2019). https://doi.org/10.1007/s10009-019-00538-y

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  • DOI: https://doi.org/10.1007/s10009-019-00538-y

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