Abstract
We present a new approach for automatic verification of data-dependent programs manipulating dynamic heaps. A heap is encoded by a graph where the nodes represent the cells, and the edges reflect the pointer structure between the cells of the heap. Each cell contains a set of variables which range over the natural numbers. Our method relies on standard backward reachability analysis, where the main idea is to use a simple set of predicates, called signatures, in order to represent bad sets of heaps. Examples of bad heaps are those which contain either garbage, lists which are not well-formed, or lists which are not sorted. We present the results for the case of programs with a single next-selector, and where variables may be compared for (in)equality. This allows us to verify for instance that a program, like bubble sort or insertion sort, returns a list which is well-formed and sorted, or that the merging of two sorted lists is a new sorted list. We report on the result of running a prototype based on the method on a number of programs.
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References
Abdulla, P.A., Annichini, A., Bouajjani, A.: Using forward reachability analysis for verification of lossy channel systems. Formal Methods in System Design (2004)
Abdulla, P.A., Atto, M., Cederberg, J., Ji, R.: Automated analysis of data-dependent programs with dynamic memory. Technical Report 2009-018, Dept. of Information Technology, Uppsala University, Sweden (2009), http://user.it.uu.se/~jonmo/datadependent.pdf
Abdulla, P.A., Bouajjani, A., Cederberg, J., Haziza, F., Rezine, A.: Monotonic abstraction for programs with dynamic memory heaps. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 341–354. Springer, Heidelberg (2008)
Abdulla, P.A., Henda, N.B., Delzanno, G., Rezine, A.: Regular model checking without transducers (on efficient verification of parameterized systems). In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 721–736. Springer, Heidelberg (2007)
Bouajjani, A., Bozga, M., Habermehl, P., Iosif, R., Moro, P., Vojnar, T.: Programs with lists are counter automata. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 517–531. Springer, Heidelberg (2006)
Bouajjani, A., Habermehl, P., Moro, P., Vojnar, T.: Verifying programs with dynamic 1-selector-linked structures in regular model checking. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 13–29. Springer, Heidelberg (2005)
Bouajjani, A., Habermehl, P., Rogalewicz, A., Vojnar, T.: Abstract tree regular model checking of complex dynamic data structures. In: Yi, K. (ed.) SAS 2006. LNCS, vol. 4134, pp. 52–70. Springer, Heidelberg (2006)
Bouajjani, A., Habermehl, P., Vojnar, T.: Abstract regular model checking. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 372–386. Springer, Heidelberg (2004)
Ganty, P., Raskin, J., Begin, L.V.: A complete abstract interpretation framework for coverability properties of wsts. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 49–64. Springer, Heidelberg (2006)
Guo, B., Vachharajani, N., August, D.I.: Shape analysis with inductive recursion synthesis. In: Proc. PLDI 2007, vol. 42 (2007)
Henriksen, J., Jensen, J., Jørgensen, M., Klarlund, N., Paige, B., Rauhe, T., Sandholm, A.: Mona: Monadic second-order logic in practice. In: Brinksma, E., Steffen, B., Cleaveland, W.R., Larsen, K.G., Margaria, T. (eds.) TACAS 1995. LNCS, vol. 1019. Springer, Heidelberg (1995)
Joshi, S., König, B.: Applying the graph minor theorem to the verification of graph transformation systems. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 214–226. Springer, Heidelberg (2008)
Laver, R.: Well-quasi-orderings and sets of finite sequences. In: Mathematical Proceedings of the Cambridge Philosophical Society, vol. 79, pp. 1–10 (1976)
Lev-Ami, T., Reps, T.W., Sagiv, S., Wilhelm, R.: Putting static analysis to work for verification: A case study. In: Proc. ISSTA 2000 (2000)
Møller, A., Schwartzbach, M.I.: The pointer assertion logic engine. In: Proc. PLDI 2001, vol. 26, pp. 221–231 (2001)
Nguyen, H.H., David, C., Qin, S., Chin, W.-N.: Automated verification of shape and size properties via separation logic. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 251–266. Springer, Heidelberg (2007)
Revesz, P.: Introduction to Constraint Databases. Springer, Heidelberg (2002)
Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: Proc. LICS 2002 (2002)
Sagiv, S., Reps, T., Wilhelm, R.: Parametric shape analysis via 3-valued logic. ACM Trans. on Programming Languages and Systems 24(3), 217–298 (2002)
Valiente, G.: Constrained tree inclusion. J. Discrete Algorithms 3(2-4), 431–447 (2005)
Yang, H., Lee, O., Berdine, J., Calcagno, C., Cook, B., Distefano, D., O’Hearn, P.W.: Scalable shape analysis for systems code. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 385–398. Springer, Heidelberg (2008)
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Abdulla, P.A., Atto, M., Cederberg, J., Ji, R. (2009). Automated Analysis of Data-Dependent Programs with Dynamic Memory. In: Liu, Z., Ravn, A.P. (eds) Automated Technology for Verification and Analysis. ATVA 2009. Lecture Notes in Computer Science, vol 5799. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04761-9_16
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DOI: https://doi.org/10.1007/978-3-642-04761-9_16
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