Abstract
We develop a taxonomy of different behavioral specification theories and expose their algebraic properties. We start by clarifying what precisely constitutes a behavioral specification theory and then introduce logical and structural operations and develop the resulting algebraic properties. In order to motivate our developments, we give plenty of examples of behavioral specification theories with different operations.
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References
Aceto, L., Fábregas, I., de Frutos-Escrig, D., Ingólfsdóttir, A., Palomino, M.: On the specification of modal systems. Sci. Comput. Program. 78(12), 2468–2487 (2013)
Aceto, L., Fokkink, W., van Glabbeek, R.J., Ingólfsdóttir, A.: Nested semantics over finite trees are equationally hard. Inf. Comput. 191(2), 203–232 (2004)
Aceto, L., Ingólfsdóttir, A., Larsen, K.G., Srba, J.: Reactive Systems. Cambridge University Press, Cambridge (2007)
Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)
Alur, R., Fix, L., Henzinger, T.A.: Event-clock automata: a determinizable class of timed automata. Theor. Comput. Sci. 211(1–2), 253–273 (1999)
Antonik, A., Huth, M., Larsen, K.G., Nyman, U., Wąsowski, A.: 20 years of modal and mixed specifications. Bull. EATCS 95, 94–129 (2008)
Bart, A., Delahaye, B., Fournier, P., Lime, D., Monfroy, E., Truchet, C.: Reachability in parametric interval Markov chains using constraints. Theor. Comput. Sci. 747, 48–74 (2018)
Bauer, S.S.: Moving from specifications to contracts in component-based design. In: de Lara, J., Zisman, A. (eds.) FASE 2012. LNCS, vol. 7212, pp. 43–58. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28872-2_3
Bauer, S.S., Fahrenberg, U., Juhl, L., Larsen, K.G., Legay, A., Thrane, C.: Quantitative refinement for weighted modal transition systems. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 60–71. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22993-0_9
Bauer, S.S., Fahrenberg, U., Juhl, L., Larsen, K.G., Legay, A., Thrane, C.: Weighted modal transition systems. Form. Meth. Syst. Des. 42(2), 193–220 (2013)
Bauer, S.S., Juhl, L., Larsen, K.G., Legay, A., Srba, J.: Extending modal transition systems with structured labels. Math. Struct. Comput. Sci. 22(4), 581–617 (2012)
Beneš, N., Černá, I., Křetínský, 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). https://doi.org/10.1007/978-3-642-24372-1_17
Beneš, N., Delahaye, B., Fahrenberg, U., Křetínský, 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. LNCS, vol. 8052, pp. 76–90. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40184-8_7
Beneš, N., Fahrenberg, U., Křetínský, J., Legay, A., Traonouez, L.-M.: Logical vs. behavioural specifications. Inf. Comput. 271, 104487 (2020)
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)
Brookes, S.D., Hoare, C.A.R., Roscoe, A.W.: A theory of communicating sequential processes. J. ACM 31(3), 560–599 (1984)
Bujtor, F., Sorokin, L., Vogler, W.: Testing preorders for dMTS. ACM Trans. Embed. Comput. Syst. 16(2), 41:1–41:28 (2017)
Bujtor, F., Vogler, W.: Failure semantics for modal transition systems. ACM Trans. Embed. Comput. Syst. 14(4), 67 (2015)
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). https://doi.org/10.1007/978-3-642-32943-2_17
David, A., Larsen, K.G., Legay, A., Nyman, U., Traonouez, L.-M., Wąsowski, A.: Real-time specifications. Softw. Tools Technol. Transf. 17(1), 17–45 (2015)
David, A., et al.: Compositional verification of real-time systems using Ecdar. Softw. Tools Technol. Transf. 14(6), 703–720 (2012)
Delahaye, B., Fahrenberg, U., Guldstrand Larsen, K., Legay, A.: Refinement and difference for probabilistic automata. In: Joshi, K., Siegle, M., Stoelinga, M., D’Argenio, P.R. (eds.) QEST 2013. LNCS, vol. 8054, pp. 22–38. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40196-1_3
Delahaye, B., Fahrenberg, U., Larsen, K.G., Legay, A.: Refinement and difference for probabilistic automata. Log. Meth. Comput. Sci. 10(3), 1–32 (2014)
Delahaye, B.: Abstract probabilistic automata. Inf. Comput. 232, 66–116 (2013)
Delahaye, B., Larsen, K.G., Legay, A., Pedersen, M.L., Wąsowski, A.: Consistency and refinement for interval Markov chains. Log. Algebr. Program. 81(3), 209–226 (2012)
Delahaye, B., Lime, D., Petrucci, L.: Parameter synthesis for parametric interval Markov chains. In: Jobstmann, B., Leino, K.R.M. (eds.) VMCAI 2016. LNCS, vol. 9583, pp. 372–390. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49122-5_18
Fahrenberg, U., Křetínský, J., Legay, A., Traonouez, L.-M.: Compositionality for quantitative specifications. Soft. Comput. 22(4), 1139–1158 (2018)
Fahrenberg, U., Legay, A.: A robust specification theory for modal event-clock automata. In: Bauer, S.S., Raclet, J.-B. (eds.) FIT 2012. EPTCS, vol. 87, pp. 5–16 (2012)
Fahrenberg, U., Legay, A.: General quantitative specification theories with modal transition systems. Acta Inf. 51(5), 261–295 (2014)
Fahrenberg, U., Legay, A.: A linear-time–branching-time spectrum of behavioral specification theories. In: Steffen, B., Baier, C., van den Brand, M., Eder, J., Hinchey, M., Margaria, T. (eds.) SOFSEM 2017. LNCS, vol. 10139, pp. 49–61. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-51963-0_5
Fahrenberg, U., Legay, A.: A linear-time-branching-time spectrum for behavioral specification theories. J. Log. Algebraic Meth. Program. 110, 100499 (2020)
Fahrenberg, U., Legay, A., Traonouez, L.-M.: Structural refinement for the modal nu-calculus. In: Ciobanu, G., Méry, D. (eds.) ICTAC 2014. LNCS, vol. 8687, pp. 169–187. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10882-7_11
Girard, J.-Y.: Linear logic. Theor. Comput. Sci. 50, 1–102 (1987)
Groote, J.F., Vaandrager, F.W.: Structured operational semantics and bisimulation as a congruence. Inf. Comput. 100(2), 202–260 (1992)
Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. J. ACM 32(1), 137–161 (1985)
Hoare, C.A.R.: Communicating sequential processes. Commun. ACM 21(8), 666–677 (1978)
Jipsen, P., Tsinakis, C.: A survey of residuated lattices. In: Martínez, J. (ed.) Ordered Algebraic Structures. Developments in Mathematics, vol. 7. Springer, Boston (2002). https://doi.org/10.1007/978-1-4757-3627-4_3
Kaynar, D.K., Lynch, N.A., Segala, R., Vaandrager, F.W.: Timed I/O automata: a mathematical framework for modeling and analyzing real-time systems. In: RTSS, pp. 166–177. IEEE Computer Society (2003)
Kaynar, D.K., Lynch, N.A., Segala, R., Vaandrager, F.W.: The Theory of Timed I/O Automata. Synthesis Lectures on Distributed Computing Theory, 2nd edn. Morgan & Claypool Publishers (2010)
Larsen, K.G.: Modal specifications. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 232–246. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-52148-8_19
Guldstrand Larsen, K.: Ideal specification formalism = expressivity + compositionality + decidability + testability + \({\ldots }\). In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 33–56. Springer, Heidelberg (1990). https://doi.org/10.1007/BFb0039050
Larsen, K.G.: Proof systems for satisfiability in Hennessy-Milner logic with recursion. Theor. Comput. Sci. 72(2&3), 265–288 (1990)
Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. In: POPL, pp. 344–352. ACM Press (1989)
Larsen, K.G., Xinxin, L.: Equation solving using modal transition systems. In: LICS, pp. 108–117. IEEE Computer Society (1990)
Pnueli, A.: Linear and branching structures in the semantics and logics of reactive systems. In: Brauer, W. (ed.) ICALP 1985. LNCS, vol. 194, pp. 15–32. Springer, Heidelberg (1985). https://doi.org/10.1007/BFb0015727
Raclet, J.-B.: Residual for component specifications. Electr. Notes Theor. Comput. Sci. 215, 93–110 (2008)
Raclet, J.-B., Badouel, E., Benveniste, A., Caillaud, B., Legay, A., Passerone, R.: A modal interface theory for component-based design. Fundam. Inf. 108(1–2), 119–149 (2011)
Segala, R., Lynch, N.A.: Probabilistic simulations for probabilistic processes. Nord. J. Comput. 2(2), 250–273 (1995)
van Glabbeek, R.J.: The linear time–branching time spectrum I, chap. 1. In: Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.) Handbook of Process Algebra, pp. 3–99. Elsevier (2001)
Vogler, W.: Failures semantics and deadlocking of modular Petri nets. Acta Inf. 26(4), 333–348 (1989)
Vogler, W. (ed.): Modular Construction and Partial Order Semantics of Petri Nets. LNCS, vol. 625. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55767-9
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Fahrenberg, U., Legay, A. (2020). Behavioral Specification Theories: An Algebraic Taxonomy. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation: Verification Principles. ISoLA 2020. Lecture Notes in Computer Science(), vol 12476. Springer, Cham. https://doi.org/10.1007/978-3-030-61362-4_14
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