Automated Program Verification

  • Azadeh Farzan
  • Matthias Heizmann
  • Jochen Hoenicke
  • Zachary Kincaid
  • Andreas Podelski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8977)

Abstract

A new approach to program verification is based on automata. The notion of automaton depends on the verification problem at hand (nested word automata for recursion, Büchi automata for termination, a form of data automata for parametrized programs, etc.). The approach is to first construct an automaton for the candidate proof and then check its validity via automata inclusion. The originality of the approach lies in the construction of an automaton from a correctness proof of a given sequence of statements. A sequence of statements is at the same time a word over a finite alphabet and it is (a very simple case of) a program. Just as we ask whether a word has an accepting run, we can ask whether a sequence of statements has a correctness proof (of a certain form). The automaton accepts exactly the sequences that do.

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References

  1. 1.
    Alur, R., Madhusudan, P.: Adding nesting structure to words. JACM 56(3) (2009)Google Scholar
  2. 2.
    Christ, J., Hoenicke, J., Nutz, A.: Proof tree preserving interpolation. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 124–138. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  3. 3.
    Demri, S., Lazić, R.: LTL with the freeze quantifier and register automata. ACM Trans. Comput. Logic 10(3), 16:1–16:30 (2009)CrossRefGoogle Scholar
  4. 4.
    Farzan, A., Kincaid, Z., Podelski, A.: Inductive data flow graphs. In: POPL, pp. 129–142. ACM (2013)Google Scholar
  5. 5.
    Farzan, A., Kincaid, Z., Podelski, A.: Proofs that count. In: POPL, pp. 151–164. ACM (2014)Google Scholar
  6. 6.
    Farzan, A., Kincaid, Z., Podelski, A.: Proof spaces for unbounded parallelism. In: POPL. ACM (2015)Google Scholar
  7. 7.
    Figueira, D.: Alternating register automata on finite words and trees. Logical Methods in Computer Science 8(1) (2012)Google Scholar
  8. 8.
    Heizmann, M., et al.: Ultimate automizer with unsatisfiable cores (competition contribution). In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 418–420. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  9. 9.
    Heizmann, M., Hoenicke, J., Leike, J., Podelski, A.: Linear ranking for linear lasso programs. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 365–380. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  10. 10.
    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) CrossRefGoogle Scholar
  11. 11.
    Heizmann, M., Hoenicke, J., Podelski, A.: Nested interpolants. In: POPL, pp. 471–482. ACM (2010)Google Scholar
  12. 12.
    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) CrossRefGoogle Scholar
  13. 13.
    Heizmann, M., Hoenicke, J., Podelski, A.: Termination analysis by learning terminating programs. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 797–813. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  14. 14.
    Junker, M., Huuck, R., Fehnker, A., Knapp, A.: SMT-based false positive elimination in static program analysis. In: Aoki, T., Taguchi, K. (eds.) ICFEM 2012. LNCS, vol. 7635, pp. 316–331. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  15. 15.
    Kaminski, M., Francez, N.: Finite-memory automata. Theor. Comput. Sci. 134(2), 329–363 (1994)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Leike, J., Heizmann, M.: Ranking templates for linear loops. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 172–186. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  17. 17.
    Neven, F., Schwentick, T., Vianu, V.: Finite state machines for strings over infinite alphabets. ACM Trans. Comput. Logic 5(3), 403–435 (2004)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Podelski, A., Rybalchenko, A.: A complete method for the synthesis of linear ranking functions. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 239–251. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  19. 19.
    Reps, T.W., Horwitz, S., Sagiv, S.: Precise interprocedural dataflow analysis via graph reachability. In: POPL, pp. 49–61. ACM (1995)Google Scholar
  20. 20.
    Schäf, M., Schwartz-Narbonne, D., Wies, T.: Explaining inconsistent code. In: ESEC/FSE, pp. 521–531. ACM (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Azadeh Farzan
    • 2
  • Matthias Heizmann
    • 1
  • Jochen Hoenicke
    • 1
  • Zachary Kincaid
    • 2
  • Andreas Podelski
    • 1
  1. 1.University of FreiburgFreiburg im BreisgauGermany
  2. 2.University of TorontoTorontoCanada

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