Shape Analysis of Single-Parent Heaps

  • Ittai Balaban
  • Amir Pnueli
  • Lenore D. Zuck
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4349)


We define the class of single-parent heap systems, which rely on a singly-linked heap in order to model destructive updates on tree structures. This encoding has the advantage of relying on a relatively simple theory of linked lists in order to support abstraction computation. To facilitate the application of this encoding, we provide a program transformation that, given a program operating on a multi-linked heap without sharing, transforms it into one over a single-parent heap. It is then possible to apply shape analysis by predicate and ranking abstraction as in [3]. The technique has been successfully applied on examples with trees of fixed arity (balancing of and insertion into a binary sort tree).


Index Variable Transition Relation Atomic Formula Predicate Abstraction Index Array 
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  1. 1.
    Arons, T., et al.: Parameterized verification with automatically computed inductive assertions. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 221–234. Springer, Heidelberg (2001)Google Scholar
  2. 2.
    Balaban, I., Pnueli, A., Zuck, L.: Shape analysis of single-parent heaps. Research Report TR2006-885, Computer Science Department, New York University, Warren Weaver Hall, Room 405, 251 Mercer St., New York, NY 10012 (November 2006)Google Scholar
  3. 3.
    Balaban, I., Pnueli, A., Zuck, L.D.: Shape analysis by predicate abstraction. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 164–180. Springer, Heidelberg (2005)Google Scholar
  4. 4.
    Balaban, I., Pnueli, A., Zuck, L.D.: Modular ranking abstraction. To appear in International Journal of Foundations of Computer Science IJFCS (2007), See
  5. 5.
    Ball, T., Jones, R.B. (eds.): CAV 2006. LNCS, vol. 4144, pp. 17–20. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  6. 6.
    Benedikt, M., Reps, T.W., Sagiv, S.: A decidable logic for describing linked data structures. In: Swierstra, S.D. (ed.) ESOP 1999 and ETAPS 1999. LNCS, vol. 1576, pp. 2–19. Springer, Berlin Heidelberg New York (1999)CrossRefGoogle Scholar
  7. 7.
    Berdine, J., et al.: Automatic termination proofs for programs with shape-shifting heaps. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 386–400. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Bingham, J.D., Rakamaric, Z.: A logic and decision procedure for predicate abstraction of heap-manipulating programs. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 207–221. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Börger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem. In: Perspectives of Mathematical Logic, 2nd edn., Springer, New York (2001)Google Scholar
  10. 10.
    Bouajjani, A., et al.: Programs with lists are counter automata. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 517–531. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Grädel, E., Otto, M., Rosen, E.: Undecidability results on two-variable logics. In: Reischuk, R., Morvan, M. (eds.) STACS 97. LNCS, vol. 1200, pp. 249–260. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  12. 12.
    Immerman, N., et al.: 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)Google Scholar
  13. 13.
    Immerman, N., et al.: Verification via structure simulation. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 281–294. Springer, Heidelberg (2004)Google Scholar
  14. 14.
    Kesten, Y., Pnueli, A.: Verification by augmented finitary abstraction. Information and Computation 163(1), 203–243 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Klarlund, N., Schwartzbach, M.I.: Graph types. In: POPL ’93: Proceedings of the 2th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pp. 196–205. ACM Press, New York (1993)CrossRefGoogle Scholar
  16. 16.
    Manevich, R., et al.: Predicate abstraction and canonical abstraction for singly-linked lists. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 181–198. Springer, Heidelberg (2005)Google Scholar
  17. 17.
    Møller, A., Schwartzbach, M.I.: The Pointer Assertion Logic Engine. In: Programming Language Design and Implementation (2001)Google Scholar
  18. 18.
    Pnueli, A., Shahar, E.: A platform combining deductive with algorithmic verification. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, p. 184. Springer, Heidelberg (1996)Google Scholar
  19. 19.
    Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: LICS, pp. 55–74. IEEE Computer Society Press, Los Alamitos (2002)Google Scholar
  20. 20.
    Wies, T., et al.: On field constraint analysis. In: Verification, Model Checking, and Abstract Interpretation (2006)Google Scholar
  21. 21.
    Yorsh, G., et al.: A logic of reachable patterns in linked data-structures. In: Aceto, L., Ingólfsdóttir, A. (eds.) FOSSACS 2006 and ETAPS 2006. LNCS, vol. 3921, pp. 94–110. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ittai Balaban
    • 1
  • Amir Pnueli
    • 1
    • 2
  • Lenore D. Zuck
    • 3
  1. 1.New York University, New York 
  2. 2.Weizmann Institute of Science 
  3. 3.University of Illinois at Chicago 

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