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Refinement of Trace Abstraction for Real-Time Programs

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Reachability Problems (RP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10506))

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Abstract

Real-time programs are made of instructions that can perform assignments to discrete and real-valued variables. They are general enough to capture interesting classes of timed systems such as timed automata, stopwatch automata, time(d) Petri nets and hybrid automata. We propose a semi-algorithm using refinement of trace abstractions to solve both the reachability verification problem and the parameter synthesis problem for real-time programs. We report on the implementation of our algorithm and we show that our new method provides solutions to problems which are unsolvable by the current state-of-the-art tools.

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Notes

  1. 1.

    As x and z are clocks their rate is always 1 and omitted in the Table.

  2. 2.

    If x was not reset by i, we would have a constraint \(x_0 = x_{-1}\), with \(x_{-1}\) unconstrained.

  3. 3.

    Uppaal terminates with the result “the language may not be empty”.

  4. 4.

    This can be done using an SMT-solver e.g., Z3.

  5. 5.

    This is the pair returned by Z3 for \(P_0 \wedge P_1 \wedge P_2\).

  6. 6.

    \(\mathcal{I}\) can be infinite but we require the control-flow graph \(\varDelta \) (transition relation) of \(A_P\) to be finite.

  7. 7.

    While difference constraints are strictly disallowed in most definitions of Timed Automata, the method we propose retain its properties regardless of their presence.

  8. 8.

    Existential quantification for the theory of Linear Real Arithmetic is within the theory via Fourier-Motzkin-elimination – hence the solver only needs support for Linear Real Arithmetic for Parameter Synthesis for Stopwatch and Timed Automata.

  9. 9.

    Proving that a system is non-robust requires proving feasibility of infinite traces for ever decreasing \(\epsilon \). We have developed some techniques to do so but this is outside of the scope of this paper.

  10. 10.

    We compare with the EFSynth-algorithm in the Imitator tool as this yielded the lowest computation time in the two terminating instances.

References

  1. Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  2. André, É., Fribourg, L., Kühne, U., Soulat, R.: IMITATOR 2.5: a tool for analyzing robustness in scheduling problems. In: Giannakopoulou, D., Méry, D. (eds.) FM 2012. LNCS, vol. 7436, pp. 33–36. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32759-9_6

    Chapter  Google Scholar 

  3. André, É., Lipari, G., Nguyen, H.G., Sun, Y.: Reachability preservation based parameter synthesis for timed automata. In: Havelund, K., Holzmann, G., Joshi, R. (eds.) NFM 2015. LNCS, vol. 9058, pp. 50–65. Springer, Cham (2015). doi:10.1007/978-3-319-17524-9_5

    Google Scholar 

  4. Behrmann, G., David, A., Larsen, K.G., Hakansson, J., Petterson, P., Yi, W., Hendriks, M.: Uppaal 4.0. In: QEST 2006, pp. 125–126 (2006)

    Google Scholar 

  5. Bérard, B., Cassez, F., Haddad, S., Lime, D., Roux, O.H.: Comparison of the expressiveness of timed automata and time Petri nets. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 211–225. Springer, Heidelberg (2005). doi:10.1007/11603009_17

    Chapter  Google Scholar 

  6. Beyer, D.: Competition on software verification. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 504–524. Springer, Heidelberg (2012). doi:10.1007/978-3-642-28756-5_38

    Chapter  Google Scholar 

  7. Bérard, B., Cassez, F., Haddad, S., Lime, D., Roux, O.H.: The expressive power of time Petri nets. Theor. Comput. Sci. 474, 1–20 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Byg, J., Jacobsen, M., Jacobsen, L., Jørgensen, K.Y., Møller, M.H., Srba, J.: TCTL-preserving translations from timed-arc Petri nets to networks of timed automata. TCS (2013). doi:10.1016/j.tcs.2013.07.011

  9. Cassez, F., Larsen, K.: The impressive power of stopwatches. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 138–152. Springer, Heidelberg (2000). doi:10.1007/3-540-44618-4_12

    Chapter  Google Scholar 

  10. Cassez, F., Roux, O.H.: Structural translation from time Petri nets to timed automata. J. Softw. Syst. 79(10), 1456–1468 (2006)

    Article  MATH  Google Scholar 

  11. Cassez, F., Sloane, A.M., Roberts, M., Pigram, M., Suvanpong, P., de Aledo, P.G.: Skink: static analysis of programs in LLVM intermediate representation - (Competition Contribution). In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10206, pp. 380–384. Springer, Heidelberg (2017). doi:10.1007/978-3-662-54580-5_27

    Chapter  Google Scholar 

  12. Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000). doi:10.1007/10722167_15

    Chapter  Google Scholar 

  13. Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008). doi:10.1007/978-3-540-78800-3_24

    Chapter  Google Scholar 

  14. Dierks, H., Kupferschmid, S., Larsen, K.G.: Automatic abstraction refinement for timed automata. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 114–129. Springer, Heidelberg (2007). doi:10.1007/978-3-540-75454-1_10

    Chapter  Google Scholar 

  15. Frehse, G.: PHAVer: algorithmic verification of hybrid systems past HyTech. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 258–273. Springer, Heidelberg (2005). doi:10.1007/978-3-540-31954-2_17

    Chapter  Google Scholar 

  16. Frehse, G., Guernic, C., Donzé, A., Cotton, S., Ray, R., Lebeltel, O., Ripado, R., Girard, A., Dang, T., Maler, O.: SpaceEx: scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22110-1_30

    Chapter  Google Scholar 

  17. Heizmann, M., Hoenicke, J., Podelski, A.: Refinement of trace abstraction. In: Palsberg, J., Su, Z. (eds.) SAS 2009. LNCS, vol. 5673, pp. 69–85. Springer, Heidelberg (2009). doi:10.1007/978-3-642-03237-0_7

    Chapter  Google Scholar 

  18. Heizmann, M., Hoenicke, J., Podelski, A.: Software model checking for people who love automata. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 36–52. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39799-8_2

    Chapter  Google Scholar 

  19. Henzinger, T.A., Ho, P.-H., Wong-toi, H.: HyTech: a model checker for hybrid systems. Softw. Tools Technol. Transf. 1, 460–463 (1997)

    MATH  Google Scholar 

  20. Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? J. Comput. Syst. Sci. 57(1), 94–124 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  21. Kordy, P., Langerak, R., Mauw, S., Polderman, J.W.: A symbolic algorithm for the analysis of robust timed automata. In: Jones, C., Pihlajasaari, P., Sun, J. (eds.) FM 2014. LNCS, vol. 8442, pp. 351–366. Springer, Cham (2014). doi:10.1007/978-3-319-06410-9_25

    Chapter  Google Scholar 

  22. Sankur, O.: Symbolic quantitative robustness analysis of timed automata. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 484–498. Springer, Heidelberg (2015). doi:10.1007/978-3-662-46681-0_48

    Google Scholar 

  23. Wang, W., Jiao, L.: Trace abstraction refinement for timed automata. In: Cassez, F., Raskin, J.-F. (eds.) ATVA 2014. LNCS, vol. 8837, pp. 396–410. Springer, Cham (2014). doi:10.1007/978-3-319-11936-6_28

    Google Scholar 

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Acknowledgments

The research leading to these results was made possible by an external stay partially funded by Otto Mønsted Fonden.

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Authors and Affiliations

  1. Department of Computing, Macquarie University, Sydney, Australia

    Franck Cassez & Peter Gjøl Jensen

  2. Department of Computer Science, Aalborg University, Aalborg, Denmark

    Peter Gjøl Jensen & Kim Guldstrand Larsen

Authors
  1. Franck Cassez
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  2. Peter Gjøl Jensen
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  3. Kim Guldstrand Larsen
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Correspondence to Peter Gjøl Jensen .

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Editors and Affiliations

  1. Royal Holloway University of London, London, United Kingdom

    Matthew Hague

  2. University of Liverpool, Liverpool, United Kingdom

    Igor Potapov

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Cassez, F., Jensen, P.G., Guldstrand Larsen, K. (2017). Refinement of Trace Abstraction for Real-Time Programs. In: Hague, M., Potapov, I. (eds) Reachability Problems. RP 2017. Lecture Notes in Computer Science(), vol 10506. Springer, Cham. https://doi.org/10.1007/978-3-319-67089-8_4

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