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A Logic and Decision Procedure for Predicate Abstraction of Heap-Manipulating Programs

  • Conference paper
Verification, Model Checking, and Abstract Interpretation (VMCAI 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3855))

Abstract

An important and ubiquitous class of programs are heap-manipulating programs (HMP), which manipulate unbounded linked data structures by following pointers and updating links. Predicate abstraction has proved to be an invaluable technique in the field of software model checking; this technique relies on an efficient decision procedure for the underlying logic. The expression and proof of many interesting HMP safety properties require transitive closure predicates; such predicates express that some node can be reached from another node by following a sequence of (zero or more) links in the data structure. Unfortunately, adding support for transitive closure often yields undecidability, so one must be careful in defining such a logic. Our primary contributions are the definition of a simple transitive closure logic for use in predicate abstraction of HMPs, and a decision procedure for this logic. Through several experimental examples, we demonstrate that our logic is expressive enough to prove interesting properties with predicate abstraction, and that our decision procedure provides us with both a time and space advantage over previous approaches.

The authors were supported by grants from the Natural Sciences and Research Council of Canada (NSERC). Jesse Bingham has moved to Intel Corporation, Hillsboro, Oregon, U.S.A.

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References

  1. Balaban, I.: personal correspondence (2005)

    Google Scholar 

  2. Balaban, I., Pnueli, A., Zuck, L.: Shape analysis by predicate abstraction. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 164–180. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  3. Ball, T., Majumdar, R., Millstein, T.D., Rajamani, S.K.: Automatic predicate abstraction of C programs. In: Conf. on Programming Language Design and Implementation (PLDI), pp. 203–213 (2001)

    Google Scholar 

  4. Ball, T., Podelski, A., Rajamani, S.K.: Relative completeness of abstraction refinement for software model checking. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, p. 158. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  5. Benedikt, M., Reps, T., Sagiv, M.: A decidable logic for describing linked data structures. In: Swierstra, S.D. (ed.) ESOP 1999. LNCS, vol. 1576, p. 2. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  6. Bingham, J., Rakamarić, Z.: A logic and decision procedure for predicate abstraction of heap-manipulating programs, UBC Dept. Comp. Sci. Tech Report TR-2005-19 (2005), http://www.cs.ubc.ca/cgi-bin/tr/2005/TR-2005-19

  7. Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. on Computers C-35(8), 677–691 (1986)

    Article  Google Scholar 

  8. Bryant, R.E., Lahiri, S.K., Seshia, S.A.: Modeling and verifying systems using a logic of counter arithmetic with lambda expressions and uninterpreted functions. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 78–92. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  9. 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)

    Chapter  Google Scholar 

  10. Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Symp. on Principles of Programming Languages (POPL), pp. 238–252 (1977)

    Google Scholar 

  11. Dams, D., Namjoshi, K.S.: Shape analysis through predicate abstraction and model checking. In: Zuck, L.D., Attie, P.C., Cortesi, A., Mukhopadhyay, S. (eds.) VMCAI 2003. LNCS, vol. 2575, pp. 310–323. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  12. Das, S., Dill, D.L.: Successive approximation of abstract transition relations. In: IEEE Symp. on Logic in Computer Science, LICS (2001)

    Google Scholar 

  13. Das, S., Dill, D.L.: Counter-example based predicate discovery in predicate abstraction. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  14. Das, S., Dill, D.L., Park, S.: Experience with predicate abstraction. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 160–171. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  15. Flanagan, C., Qadeer, S.: Predicate abstraction for software verification. In: Symp. on Principles of Programming Languages (POPL), pp. 191–202 (2002)

    Google Scholar 

  16. Graf, S., Saidi, H.: Construction of abstract state graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254. Springer, Heidelberg (1997)

    Google Scholar 

  17. Gries, D.: The Science of Programming. Springer, New York (1981)

    MATH  Google Scholar 

  18. Henzinger, T.A., Jhala, R., Majumdar, R., Sutre, G.: Lazy abstraction. In: Symp. on Principles of Programming Languages (POPL), pp. 58–70 (2002)

    Google Scholar 

  19. Immerman, N., Rabinovich, A., Reps, T., Sagiv, M., Yorsh, G.: The boundary between decidability and undecidability for transitive closure logics. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 160–174. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  20. Jensen, J.L., Jørgensen, M.E., Klarlund, N., Schwartzbach, M.I.: Automatic verification of pointer programs using monadic second-order logic. In: Conf. on Programming Language Design and Implementation (PLDI), pp. 226–236 (1997)

    Google Scholar 

  21. Kesten, Y., Pnueli, A.: Verification by augmented finitary abstraction. Information and Computation 163(1), 203–243 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  22. Klarlund, N., Schwartzbach, M.I.: Graph types. In: Symp. on Principles of Programming Languages (POPL), pp. 196–205 (1993)

    Google Scholar 

  23. Lahiri, S.K., Qadeer, S.: Verifying properties of well-founded linked lists, Microsoft Research Tech Report MSR-TR-2005-97 (2005)

    Google Scholar 

  24. Lev-Ami, T., Reps, T., Sagiv, M., Wilhelm, R.: Putting static analysis to work for verification: A case study. In: Intl. Symp. on Software Testing and Analysis, pp. 26–38 (2000)

    Google Scholar 

  25. Lev-Ami, T., Sagiv, M.: TVLA: A system for implementing static analyses. In: Palsberg, J. (ed.) SAS 2000. LNCS, vol. 1824, pp. 280–301. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  26. Loginov, A., Reps, T.W., Sagiv, S.: Abstraction refinement via inductive learning. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 519–533. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  27. Manevich, R., Yahav, E., Ramalingam, G., Sagiv, M.: Predicate abstraction and canonical abstraction for singly-linked lists. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 181–198. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  28. McPeak, S., Necula, G.C.: Data structure specifications via local equality axioms. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 476–490. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  29. Møller, A., Schwartzbach, M.I.: The pointer assertion logic engine. In: Conf. on Programming Language Design and Implementation (PLDI), pp. 221–231 (2001)

    Google Scholar 

  30. Nelson, G.: Techniques for program verification. PhD thesis, Stanford University (1979)

    Google Scholar 

  31. Nelson, G.: Verifying reachability invariants of linked structures. In: Symp. on Principles of Programming Languages (POPL), pp. 38–47 (1983)

    Google Scholar 

  32. Sagiv, M., Reps, T., Wilhelm, R.: Parametric shape analysis via 3-valued logic. ACM Trans. on Programming Languages and Systems 24(3), 217–298 (2002)

    Article  Google Scholar 

  33. Yorsh, G., Reps, T., Sagiv, M.: Symbolically computing most-precise abstract operations for shape analysis. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 530–545. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of British Columbia, Canada

    Jesse Bingham & Zvonimir Rakamarić

Authors
  1. Jesse Bingham
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  2. Zvonimir Rakamarić
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Editor information

Editors and Affiliations

  1. Aiken Computation Laboratory, Harvard University,, 02138, Cambridge, Mass, USA

    E. Allen Emerson

  2. Bell Laboratories, Alcatel-Lucent,  

    Kedar S. Namjoshi

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Bingham, J., Rakamarić, Z. (2005). A Logic and Decision Procedure for Predicate Abstraction of Heap-Manipulating Programs. In: Emerson, E.A., Namjoshi, K.S. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2006. Lecture Notes in Computer Science, vol 3855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11609773_14

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  • DOI: https://doi.org/10.1007/11609773_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31139-3

  • Online ISBN: 978-3-540-31622-0

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