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Constrained Dynamic Tree Networks

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Reachability Problems (RP 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11123))

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Abstract

We generalise Constrained Dynamic Pushdown Networks, introduced by Bouajjani et al., to Constrained Dynamic Tree Networks. In this model, we have trees of processes which may monitor their children. We allow the processes to be defined by any computation model for which the alternating reachability problem is decidable. We address the problem of symbolic reachability analysis for this model. More precisely, we consider the problem of computing an effective representation of their reachability sets using finite state automata. We show that backwards reachability sets starting from regular sets of configurations are always regular. We provide an algorithm for computing backwards reachability sets using tree automata.

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Notes

  1. 1.

    If it is not the case, we create a copy of these states on which we conserve all the transition as an “internal state”, and remove the incoming transitions to these states.

  2. 2.

    If so, for a state \(s_r\), we create a new final state \(s\) and add the transition \(s_r\xrightarrow {\mathrm {Id}} s\), and remove \(s_r\) from the set of final states.

References

  1. Bouajjani, A., Esparza, J., Maler, O.: Reachability analysis of pushdown automata: application to model-checking. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 135–150. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-63141-0_10

    Chapter  Google Scholar 

  2. Bouajjani, A., Müller-Olm, M., Touili, T.: Regular symbolic analysis of dynamic networks of pushdown systems. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 473–487. Springer, Heidelberg (2005). https://doi.org/10.1007/11539452_36

    Chapter  Google Scholar 

  3. Brainerd, W.S.: Tree generating regular systems. Inf. Control 14(2), 217–231 (1969)

    Article  MathSciNet  Google Scholar 

  4. Broadbent, C.H., Carayol, A., Hague, M., Serre, O.: A saturation method for collapsible pushdown systems. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012. LNCS, vol. 7392, pp. 165–176. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31585-5_18

    Chapter  Google Scholar 

  5. Broadbent, C.H., Carayol, A., Hague, M., Serre, O.: C-SHORe: a collapsible approach to higher-order verification. In: ICFP (2013)

    Google Scholar 

  6. Broadbent, C.H., Kobayashi, N.: Saturation-based model checking of higher-order recursion schemes. In: CSL (2013)

    Google Scholar 

  7. Chadha, R., Viswanathan, M.: Decidability results for well-structured transition systems with auxiliary storage. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 136–150. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74407-8_10

    Chapter  Google Scholar 

  8. Clemente, L., Parys, P., Salvati, S., Walukiewicz, I.: Ordered tree-pushdown systems. In: FSTTCS (2015)

    Google Scholar 

  9. Clemente, L., Parys, P., Salvati, S., Walukiewicz, I.: The diagonal problem for higher-order recursive schemes is decidable. In: LICS (2016)

    Google Scholar 

  10. Cyriac, A., Gastin, P., Kumar, K.N.: MSO decidability of multi-pushdown systems via split-width. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 547–561. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32940-1_38

    Chapter  Google Scholar 

  11. Gawlitza, T.M., Lammich, P., Müller-Olm, M., Seidl, H., Wenner, A.: Join-lock-sensitive forward reachability analysis for concurrent programs with dynamic process creation. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 199–213. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-18275-4_15

    Chapter  Google Scholar 

  12. Hague, M.: Saturation of concurrent collapsible pushdown systems. In: FSTTCS (2013)

    Google Scholar 

  13. Hague, M., Kochems, J., Ong, C.-H.L.: Unboundedness and downward closures of higher-order pushdown automata. In: POPL (2016)

    Google Scholar 

  14. Hague, M., Murawski, A.S., Ong, C.-H.L., Serre, O.: Collapsible pushdown automata and recursion schemes. In: LICS (2008)

    Google Scholar 

  15. Hague, M., Ong, C.-H.L.: Winning regions of pushdown parity games: a saturation method. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 384–398. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04081-8_26

    Chapter  Google Scholar 

  16. Hague, M., Penelle, V.: Constrained dynamic tree networks (2018). https://doi.org/10.17637/rh.6850508, https://figshare.com/articles/main_pdf/6850508

  17. Kobayashi, N.: Model-checking higher-order functions. In: PPDP (2009)

    Google Scholar 

  18. Kobayashi, N.: Higher-order model checking: from theory to practice. In: LICS (2011)

    Google Scholar 

  19. Kobayashi, N.: A practical linear time algorithm for trivial automata model checking of higher-order recursion schemes. In: Hofmann, M. (ed.) FoSSaCS 2011. LNCS, vol. 6604, pp. 260–274. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19805-2_18

    Chapter  Google Scholar 

  20. Kobayashi, N., Igarashi, A.: Model-checking higher-order programs with recursive types. In: Felleisen, M., Gardner, P. (eds.) ESOP 2013. LNCS, vol. 7792, pp. 431–450. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-37036-6_24

    Chapter  Google Scholar 

  21. Kobayashi, N.: GTRecS2: a model checker for recursion schemes based on games and types (2012). http://www-kb.is.s.u-tokyo.ac.jp/~koba/gtrecs2/

  22. La Torre, S., Muscholl, A., Walukiewicz, I.: Safety of parametrized asynchronous shared-memory systems is almost always decidable. In: CONCUR (2015)

    Google Scholar 

  23. Lammich, P., Müller-Olm, M., Wenner, A.: Predecessor sets of dynamic pushdown networks with tree-regular constraints. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 525–539. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02658-4_39

    Chapter  Google Scholar 

  24. Lammich, P., Müller-Olm, M., Seidl, H., Wenner, A.: Contextual locking for dynamic pushdown networks. In: Logozzo, F., Fähndrich, M. (eds.) SAS 2013. LNCS, vol. 7935, pp. 477–498. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38856-9_25

    Chapter  Google Scholar 

  25. Löding, C.: Infinite graphs generated by tree rewriting. Ph.D. thesis, RWTH Aachen (2003)

    Google Scholar 

  26. Lugiez, D.: Forward analysis of dynamic network of pushdown systems is easier without order. Int. J. Found. Comput. Sci. 22(4), 843–862 (2011)

    Article  MathSciNet  Google Scholar 

  27. Lugiez, D., Schnoebelen, P.: The regular viewpoint on PA-processes. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 50–66. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0055615

    Chapter  Google Scholar 

  28. Madhusudan, P., Parlato, G.: The tree width of auxiliary storage. In: POPL (2011)

    Google Scholar 

  29. Muscholl, A., Seidl, H., Walukiewicz, I.: Reachability for dynamic parametric processes. In: Bouajjani, A., Monniaux, D. (eds.) VMCAI 2017. LNCS, vol. 10145, pp. 424–441. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-52234-0_23

    Chapter  Google Scholar 

  30. Neatherway, R.P., Ramsay, S.J., Ong, C.-H.L.: A traversal-based algorithm for higher-order model checking. In: ICFP (2012)

    Google Scholar 

  31. Nordhoff, B., Müller-Olm, M., Lammich, P.: Iterable forward reachability analysis of monitor-DPNs. In: Semantics, Abstract Interpretation, and Reasoning About Programs: Essays Dedicated to David A. Schmidt on the Occasion of his Sixtieth Birthday (2013)

    Google Scholar 

  32. Ong, C.-H.L.: On model-checking trees generated by higher-order recursion schemes. In: LICS (2006)

    Google Scholar 

  33. Parys, P.: The complexity of the diagonal problem for recursion schemes. In: FSTTCS (2018)

    Google Scholar 

  34. Penelle, V.: Rewriting higher-order stack trees. In: Beklemishev, L.D., Musatov, D.V. (eds.) CSR 2015. LNCS, vol. 9139, pp. 364–397. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20297-6_24

    Chapter  Google Scholar 

  35. Qadeer, S., Rehof, J.: Context-bounded model checking of concurrent software. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 93–107. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31980-1_7

    Chapter  MATH  Google Scholar 

  36. Ramsay, S.J., Neatherway, R.P., Ong, C.-H.L.: A type-directed abstraction refinement approach to higher-order model checking. In: POPL (2014)

    Google Scholar 

  37. Schwoon, S.: Model-checking pushdown systems. Ph.D. thesis, Technical University of Munich (2002)

    Google Scholar 

  38. Seth, A.: Games on higher order multi-stack pushdown systems. In: Bournez, O., Potapov, I. (eds.) RP 2009. LNCS, vol. 5797, pp. 203–216. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04420-5_19

    Chapter  Google Scholar 

  39. Song, F., Touili, T.: Model checking dynamic pushdown networks. Form. Asp. Comput. 27(2), 397–421 (2015)

    Article  MathSciNet  Google Scholar 

  40. Suwimonteerabuth, D., Berger, F., Schwoon, S., Esparza, J.: jMoped: a test environment for java programs. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 164–167. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73368-3_19

    Chapter  Google Scholar 

  41. Touili, T., Atig, M.F.: Verifying parallel programs with dynamic communication structures. Theor. Comput. Sci. 411(38–39), 3460–3468 (2010)

    Article  MathSciNet  Google Scholar 

  42. Yasukata, K., Kobayashi, N., Matsuda, K.: Pairwise reachability analysis for higher order concurrent programs by higher-order model checking. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014. LNCS, vol. 8704, pp. 312–326. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44584-6_22

    Chapter  Google Scholar 

  43. Yasukata, K., Tsukada, T., Kobayashi, N.: Verification of higher-order concurrent programs with dynamic resource creation. In: Igarashi, A. (ed.) APLAS 2016. LNCS, vol. 10017, pp. 335–353. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-47958-3_18

    Chapter  Google Scholar 

  44. Zetzsche, G.: An approach to computing downward closures. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 440–451. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47666-6_35

    Chapter  Google Scholar 

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Acknowledgement

We thank the anonymous reviewers for their remarks. This work was supported by the Engineering and Physical Sciences Research Council [EP/K009907/1].

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Authors and Affiliations

  1. Royal Holloway, University of London, Egham, UK

    Matthew Hague

  2. Université de Bordeaux, LaBRI, UMR 5800, Talence, France

    Vincent Penelle

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  1. Matthew Hague
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Correspondence to Matthew Hague .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, UK

    Igor Potapov

  2. Aix-Marseille University, Marseille, France

    Pierre-Alain Reynier

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Hague, M., Penelle, V. (2018). Constrained Dynamic Tree Networks. In: Potapov, I., Reynier, PA. (eds) Reachability Problems. RP 2018. Lecture Notes in Computer Science(), vol 11123. Springer, Cham. https://doi.org/10.1007/978-3-030-00250-3_4

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  • DOI: https://doi.org/10.1007/978-3-030-00250-3_4

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