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Antichains for the Verification of Recursive Programs

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Networked Systems (NETYS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 9466))

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Abstract

Safety verification of while programs is often phrased in terms of inclusions \(L(A)\subseteq L(B)\) among regular languages. Antichain-based algorithms have been developed as an efficient method to check such inclusions. In this paper, we generalize the idea of antichain-based verification to verifying safety properties of recursive programs. To be precise, we give an antichain-based algorithm for checking inclusions of the form \(L(G)\subseteq L(B)\), where \(G\) is a context-free grammar and \(B\) is a finite automaton. The idea is to phrase the inclusion as a data flow analysis problem over a relational domain. In a second step, we generalize the approach towards bounded context switching.

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References

  1. Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.-K.: General decidability theorems for infinite-state systems. In: LICS, pp. 313–321. IEEE (1996)

    Google Scholar 

  2. Atig, M.F., Bouajjani, A., Parlato, G.: Getting rid of store-buffers in TSO analysis. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 99–115. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  3. Büchi, J.R.: On a decision method in restricted second order arithmetic. In: Lane, S.M., Siefkes, D. (eds.) The Collected Works of J. Richard Büchi. Springer, New York (1990)

    Google Scholar 

  4. Bouajjani, A., Esparza, J., Touili, T.: A generic approach to the static analysis of concurrent programs with procedures. In: POPL, pp. 62–73. ACM (2003)

    Google Scholar 

  5. Bruyère, V., Ducobu, M., Gauwin, O.: Visibly pushdown automata: universality and inclusion via antichains. In: Dediu, A.-H., Martín-Vide, C., Truthe, B. (eds.) LATA 2013. LNCS, vol. 7810, pp. 190–201. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  6. Cousot, P., Cousot, R.: Automatic synthesis of optimal invariant assertions: mathematical foundations. In: Artificial Intelligence and Programming Languages, pp. 1–12. ACM (1977)

    Google Scholar 

  7. De Wulf, M., Doyen, L., Raskin, J.-F.: A lattice theory for solving games of imperfect information. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 153–168. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  8. Esparza, J., Kiefer, S., Luttenberger, M.: Newtonian program analysis. JACM 57(6), 33:1–33:47 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Farzan, A., Kincaid, Z., Podelski, A.: Inductive data flow graphs. In: POPL, pp. 129–142. ACM (2013)

    Google Scholar 

  10. Farzan, A., Kincaid, Z., Podelski, A.: Proofs that count. In: POPL, pp. 151–164. ACM (2014)

    Google Scholar 

  11. Farzan, A., Kincaid, Z., Podelski, A.: Proof spaces for unbounded parallelism. In: POPL, pp. 407–420. ACM (2015)

    Google Scholar 

  12. Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere!. Theor. Comput. Sci. 256(1–2), 63–92 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. Fogarty, S., Vardi, M.Y.: Efficient Büchi universality checking. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 205–220. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  14. Friedmann, O., Klaedtke, F., Lange, M.: Ramsey goes visibly pushdown. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part II. LNCS, vol. 7966, pp. 224–237. Springer, Heidelberg (2013)

    Google Scholar 

  15. Heizmann, M., Hoenicke, J., Podelski, A.: Nested interpolants. In: POPL, pp. 471–482. ACM (2010)

    Google Scholar 

  16. 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)

    Chapter  Google Scholar 

  17. Lal, A., Touili, T., Kidd, N., Reps, T.: Interprocedural analysis of concurrent programs under a context bound. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 282–298. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  18. Long, Z., Calin, G., Majumdar, R., Meyer, R.: Language-theoretic abstraction refinement. In: de Lara, J., Zisman, A. (eds.) FASE 2012. LNCS, vol. 7212, pp. 362–376. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  19. Nielson, F., Nielson, H.R., Hankin, C.: Principles of Program Analysis. Springer, Heidelberg (1999)

    Book  MATH  Google Scholar 

  20. 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)

    Chapter  Google Scholar 

  21. Ramalingam, G.: Context-sensitive synchronization-sensitive analysis is undecidable. ACM Trans. Program. Lang. Syst. 22(2), 416–430 (2000)

    Article  Google Scholar 

  22. Reps, T., Horwitz, S., Sagiv, M.: Precise interprocedural dataflow analysis via graph reachability. In: POPL, pp. 49–61. ACM (1995)

    Google Scholar 

  23. Seidl, H., Wilhelm, R., Hack, S.: Compiler Design - Analysis and Transformation. Springer, Heidelberg (2012)

    Book  MATH  Google Scholar 

  24. Sharir, M., Pnueli, A.: Two approaches to interprocedural data flow analysis. Technical report 2, New York University (1978)

    Google Scholar 

  25. De Wulf, M., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Antichains: a new algorithm for checking universality of finite automata. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 17–30. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

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Acknowledgement

This work was supported by the DFG project R2M2: Robustness against Relaxed Memory Models, the Czech Science Foundation (projects 14-11384S and 202/13/37876P), the BUT FIT project FIT-S-14-2486, and the EU/Czech IT4Innovations Centre of Excellence project CZ.1.05/1.1.00/02.0070.

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Authors and Affiliations

  1. Brno University of Technology, Brno, Czech Republic

    Lukáš Holík

  2. University of Kaiserslautern, Kaiserslautern, Germany

    Roland Meyer

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  1. Lukáš Holík
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  2. Roland Meyer
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Correspondence to Lukáš Holík .

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Editors and Affiliations

  1. Université Paris Diderot, Paris Cedex 13, France

    Ahmed Bouajjani

  2. Université Paris Diderot, Paris Cedex 13, France

    Hugues Fauconnier

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Holík, L., Meyer, R. (2015). Antichains for the Verification of Recursive Programs. In: Bouajjani, A., Fauconnier, H. (eds) Networked Systems . NETYS 2015. Lecture Notes in Computer Science(), vol 9466. Springer, Cham. https://doi.org/10.1007/978-3-319-26850-7_22

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  • DOI: https://doi.org/10.1007/978-3-319-26850-7_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26849-1

  • Online ISBN: 978-3-319-26850-7

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