Quotient of Acceptance Specifications Under Reachability Constraints

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8977)


The quotient operation, which is dual to the composition, is crucial in specification theories as it allows the synthesis of missing specifications and thus enables incremental design. In this paper, we consider a specification theory based on marked acceptance specifications (MAS) which are automata enriched with variability information encoded by acceptance sets and with reachability constraints on states. We define a sound and complete quotient for MAS hence ensuring reachability properties by construction.


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  1. 1.
    Bauer, S.S., Fahrenberg, U., Juhl, L., Larsen, K.G., Legay, A., Thrane, C.R.: Weighted modal transition systems. Formal Methods in System Design 42(2), 193–220 (2013)CrossRefMATHGoogle Scholar
  2. 2.
    Bauer, S.S., Larsen, K.G., Legay, A., Nyman, U., Wasowski, A.: A modal specification theory for components with data. Sci. Comput. Program. 83, 106–128 (2014)CrossRefGoogle Scholar
  3. 3.
    Beneš, N., Delahaye, B., Fahrenberg, U., Křet\’ınský, J., Legay, A.: Hennessy-Milner Logic with Greatest Fixed Points as a Complete Behavioural Specification Theory. In: D’Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013 – Concurrency Theory. LNCS, vol. 8052, pp. 76–90. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  4. 4.
    Beneš, N., Černá, I., Křet\’ınský, J.: Modal Transition Systems: Composition and LTL Model Checking. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 228–242. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  5. 5.
    Beneš, N., Křet\’ınský, J., Larsen, K.G., Møller, M.H., Srba, J.: Parametric Modal Transition Systems. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 275–289. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  6. 6.
    Benveniste, A., Raclet, J.B., Caillaud, B., Nickovic, D., Passerone, R., Sangiovanni-Vincentelli, A., Henzinger, T., Larsen, K.G.: Contracts for the design of embedded systems - part II: theory (2012)Google Scholar
  7. 7.
    Bertrand, N., Legay, A., Pinchinat, S., Raclet, J.B.: Modal event-clock specifications for timed component-based design. Sci. Comput. Program. 77(12), 1212–1234 (2012)CrossRefMATHGoogle Scholar
  8. 8.
    Caillaud, B., Raclet, J.-B.: Ensuring Reachability by Design. In: Roychoudhury, A., D’Souza, M. (eds.) ICTAC 2012. LNCS, vol. 7521, pp. 213–227. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  9. 9.
    Chen, T., Chilton, C., Jonsson, B., Kwiatkowska, M.: A Compositional Specification Theory for Component Behaviours. In: Seidl, H. (ed.) Programming Languages and Systems. LNCS, vol. 7211, pp. 148–168. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  10. 10.
    Darondeau, P., Dubreil, J., Marchand, H.: Supervisory control for modal specifications of services. In: WODES. pp. 428–435 (2010)Google Scholar
  11. 11.
    David, A., Larsen, K.G., Legay, A., Nyman, U., Wasowski, A.: Timed I/O automata : A complete specification theory for real-time systems. In: HSCC. pp. 91–100. ACM (2010)Google Scholar
  12. 12.
    Hennessy, M.: Acceptance trees. J. ACM 32(4), 896–928 (1985)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Larsen, K.G., Thomsen, B.: A modal process logic. In: LICS. pp. 203–210. IEEE (1988)Google Scholar
  14. 14.
    Lüttgen, G., Vogler, W.: Modal interface automata. Logical Methods in Computer Science 9(3) (2013)Google Scholar
  15. 15.
    Raclet, J.B.: Residual for component specifications. FACS. Electr. Notes Theor. Comput. Sci. 215, 93–110 (2008)CrossRefGoogle Scholar
  16. 16.
    Raclet, J.B., Badouel, E., Benveniste, A., Caillaud, B., Legay, A., Passerone, R.: A modal interface theory for component-based design. Fun. Informaticae 108(1–2), 119–149 (2011)MATHMathSciNetGoogle Scholar
  17. 17.
    Verdier, G., Raclet, J.B.: Quotient of acceptance specifications under reachability constraints. arXiv:1411.6463 (2014)

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.IRIT/CNRSToulouse Cedex 9France

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