Abstract
We develop a new method for determining the consistency of timed scenarios. If the scenario is consistent, we obtain a canonical representation for the entire class of equivalent scenarios. This allows us to optimise a scenario according to various criteria. In particular, we are able to minimize the largest constant in the scenario’s set of constraints: this technique is directly relevant to decreasing the costs of verification for timed automata synthesized from timed scenarios.
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Notes
- 1.
Most model-checking tools for timed automata (e.g., UPPAAL [7] and KRONOS [9]) use region-based and zone-based abtraction methods in order to make verification possible in spite of the infinite state spaces of timed automata. It is well-known that both of these abstraction methods depend on the number of clocks and on the size of the constants that appear in constraints. In fact, the size of the region graph is exponential in the number of clocks and the (encoding of) constants [3].
- 2.
Behaviours are essentially the “timed words” of Alur [2].
- 3.
To keep the presentation compact, we do not allow sharp inequalities: allowing them would complicate our definitions and proofs, without affecting the general principles. Notice that sharp inequalities are of mainly theoretical interest: in practice we can measure time only with some finite granularity \(\gamma \), so \(x < c\) is for all practical purposes equivalent to \(x \le c - \gamma \).
- 4.
There is nothing new in the intuition that a scenario describes a set of behaviours: see, e.g., the paper by Somé et al. [20].
- 5.
The other way is to increase \(M_{0 1}\) to 4, but that would introduce new behaviours.
- 6.
As elsewhere, \(t_{ij} = t_j - t_i\).
- 7.
If \(h_{ij} = \infty \) then \(t_{ij}^{\mathcal {B^H}}\) can be an arbitrary number not smaller than \(l_{ij}\).
- 8.
We are only proving the existence of such a behaviour. A method of actually constructing it is discussed in Sect. 3.3.
- 9.
The values in the table are rational numbers, but they have a least common denominator. Adding or subtracting two such values cannot produce a result that does not share that common denominator. So our algorithm cannot decrease the difference between two such values indefinitely without making it negative.
- 10.
For example, (R5) depends on \(h_{ik}\) and \(l_{jk}\), which can be changed by (R6) and (R3). But if (R5) is applicable, i.e., if \(h_{ij} + l_{jk} > h_{ik}\) holds, then (R6) is not applicable: we cannot have \(h_{ik} > h_{ij} + h_{jk}\), because \(l_{jk} \le h_{jk}\) (the table is valid); similarly, (R3) is not applicable: \(l_{ik} > h_{ij} + l_{jk}\) would imply \(l_{ik} > h_{ik}\).
- 11.
In practice it is often convenient to pinpoint the first “offending” constraint that makes a scenario inconsistent. This is easily done by making sure that the order of constraints in \(\varPsi \) corresponds to the textual order of constraints in the scenario, and attempting to stabilise the table each time a new constraint is added to it. If the number of constraints is proportional to n, the cost becomes \(O(n^4)\).
- 12.
If the attempt to do so fails because of the inconsistency of \(\xi \), then producing an equivalent scenario with smaller constants is trivial (and probably pointless).
- 13.
More formally, we create a finite sequence of scenarios, \(\eta ^0 \eta ^1 \ldots \) and a corresponding sequence of tables, \(\mathcal {D}^{\eta ^0}\mathcal {D}^{\eta ^1}\ldots \). We felt that a more pedantic presentation would be harder to follow.
References
Akshay, S., Mukund, M., Kumar, K.N.: Checking coverage for infinite collections of timed scenarios. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 181–196. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74407-8_13
Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)
Alur, R., Madhusudan, P.: Decision problems for timed automata: a survey. In: Bernardo, M., Corradini, F. (eds.) SFM-RT 2004. LNCS, vol. 3185, pp. 1–24. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30080-9_1
Alur, R., Martin, M., Raghothaman, M., Stergiou, C., Tripakis, S., Udupa, A.: Synthesizing finite-state protocols from scenarios and requirements. In: Yahav, E. (ed.) HVC 2014. LNCS, vol. 8855, pp. 75–91. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-13338-6_7
Ben-Abdallah, H., Leue, S.: Timing constraints in Message Sequence Chart specifications. In: Togashi, A., Mizuno, T., Shiratori, N., Higashino, T. (eds.) FORTE. IFIP Conference Proceedings, vol. 107, pp. 91–106. Chapman & Hall, London (1997)
Bengtsson, J.: Clocks, DBMs and states in timed systems. Ph.D. thesis, Uppsala University (2002)
Bengtsson, J., Larsen, K., Larsson, F., Pettersson, P., Yi, W.: UPPAAL — a tool suite for automatic verification of real-time systems. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds.) HS 1995. LNCS, vol. 1066, pp. 232–243. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0020949
Bollig, B., Katoen, J.-P., Kern, C., Leucker, M.: Replaying play in and play out: synthesis of design models from scenarios by learning. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 435–450. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71209-1_33
Bozga, M., Daws, C., Maler, O., Olivero, A., Tripakis, S., Yovine, S.: Kronos: a model-checking tool for real-time systems. In: Hu, A.J., Vardi, M.Y. (eds.) CAV 1998. LNCS, vol. 1427, pp. 546–550. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0028779
Damas, C., Lambeau, B., Roucoux, F., van Lamsweerde, A.: Analyzing critical process models through behavior model synthesis. In: Proceedings of the 31st International Conference on Software Engineering, pp. 441–451. IEEE Computer Society (2009)
Dill, D.L.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-52148-8_17
En-Nouaary, A., Dssouli, R., Khendek, F.: From timed scenarios to SDL: specification, implementation and testing of real-time systems. In: SDL Forum, p. 67 (1999)
Giese, H.: Towards scenario-based synthesis for parametric timed automata. In: Proceedings of the 2nd International Workshop on Scenarios and State Machines: Models, Algorithms, and Tools (SCESM), Portland, USA (2003)
Harel, D., Kugler, H.: Synthesizing state-based object systems from LSC specifications. In: Yu, S., Păun, A. (eds.) CIAA 2000. LNCS, vol. 2088, pp. 1–33. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44674-5_1
Harel, D., Kugler, H., Pnueli, A.: Synthesis revisited: generating statechart models from scenario-based requirements. In: Kreowski, H.-J., Montanari, U., Orejas, F., Rozenberg, G., Taentzer, G. (eds.) Formal Methods in Software and Systems Modeling. LNCS, vol. 3393, pp. 309–324. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31847-7_18
Heitmeyer, C.L., et al.: Building high assurance human-centric decision systems. Autom. Softw. Eng. 22(2), 159–197 (2015)
Mahfoudh, M., Niebert, P., Asarin, E., Maler, O.: A satisfiability checker for difference logic. In: Fifth International Symposium on the Theory and Applications of Satisfiability Testing (2002)
Nieuwenhuis, R., Oliveras, A.: DPLL(T) with exhaustive theory propagation and its application to difference logic. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 321–334. Springer, Heidelberg (2005). https://doi.org/10.1007/11513988_33
Saeedloei, N., Kluźniak, F.: From scenarios to timed automata. In: Cavalheiro, S., Fiadeiro, J. (eds.) SBMF 2017. LNCS, vol. 10623, pp. 33–51. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70848-5_4
Somé, S., Dssouli, R., Vaucher, J.: From scenarios to timed automata: building specifications from users requirements. In: Proceedings of the Second Asia Pacific Software Engineering Conference, APSEC 1995, pp. 48–57. IEEE Computer Society, Washington, DC, USA (1995)
Uchitel, S., Kramer, J., Magee, J.: Synthesis of behavioral models from scenarios. IEEE Trans. Softw. Eng. 29(2), 99–115 (2003)
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Saeedloei, N., Kluźniak, F. (2018). Timed Scenarios: Consistency, Equivalence and Optimization. In: Massoni, T., Mousavi, M. (eds) Formal Methods: Foundations and Applications. SBMF 2018. Lecture Notes in Computer Science(), vol 11254. Springer, Cham. https://doi.org/10.1007/978-3-030-03044-5_14
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