Abstract
We define a logic, called CSL, for the specification of complex data structures, and we show its use in program verification. Our framework allows to handle programs with dynamic linked structures and arrays carrying unbounded data, as well as the composition of these structures. The formulas in CSL allow a limited form of alternation between existential and universal quantifiers and they can express (1) constraints on reachability between positions in the heap following some pointer fields, (2) linear constraints on the lengths of the lists and the indexes of the arrays, and (3) constraints on the values of the data attached to these positions. For data constraints, the logic CSL is parameterized by a first-order logic over the considered data domain. We prove that the satisfiability problem of CSL is decidable whenever the underlying data logic is decidable and that CSL is closed under the computation of the strongest post-condition in the considered class of programs.
Partially supported by the french ANR project AVERISS and the RNTL project AVERILES.
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References
Balaban, I., Pnueli, A., Zuck, L.D.: Shape analysis of single-parent heaps. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 91–105. Springer, Heidelberg (2007)
Benedikt, M., Reps, T.W., Sagiv, S.: A decidable logic for describing linked data structures. In: Swierstra, S.D. (ed.) ESOP 1999. LNCS, vol. 1576, pp. 2–19. Springer, Heidelberg (1999)
Berdine, J., Calcagno, C., Cook, B., Distefano, D., O’Hearn, P.W., Wies, T., Yang, H.: Shape analysis for composite data structures. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 178–192. Springer, Heidelberg (2007)
Berdine, J., Calcagno, C., O’Hearn, P.W.: A decidable fragment of separation logic. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 97–109. Springer, Heidelberg (2004)
Blanco, V., Puerto, J.: Short rational generating functions for multiobjective linear integer programming. arXiv:0712.4295v3 (2008)
Borger, E., Gradel, E., Gurevich, Y.: The Classical Decision Problem. Perspectives of Mathematical Logic. Springer, Heidelberg (1997)
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., Drăgoi, C., Enea, C., Sighireanu, M.: A logic-based framework for reasoning about composite data structures. Technical report. LIAFA, University Paris 7 & CNRS
Bouajjani, A., Habermehl, P., Jurski, Y., Sighireanu, M.: Rewriting systems with data. In: Csuhaj-Varjú, E., Ésik, Z. (eds.) FCT 2007. LNCS, vol. 4639, pp. 1–22. Springer, Heidelberg (2007)
Bouajjani, A., Habermehl, P., Rogalewicz, A., Vojnar, T.: Abstract regular tree model checking of complex dynamic data structures. In: Yi, K. (ed.) SAS 2006. LNCS, vol. 4134, pp. 52–70. Springer, Heidelberg (2006)
Bradley, A.R., Manna, Z., Sipma, H.B.: What’s decidable about arrays? In. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 427–442. Springer, Heidelberg (2005)
Ehrgott, M.: A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spectrum 22(4), 425–460 (2000)
Habermehl, P., Iosif, R., Vojnar, T.: What else is decidable about integer arrays? In. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 474–489. Springer, Heidelberg (2008)
Lahiri, S.K., Qadeer, S.: Back to the future: revisiting precise program verification using \(\mbox{SMT}\) solvers. In: POPL, pp. 171–182. ACM, New York (2008)
Møller, A., Schwartzbach, M.I.: The pointer assertion logic engine. In: PLDI, pp. 221–231. ACM, New York (2001)
Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: LICS, pp. 55–74. IEEE Computer Society, Los Alamitos (2002)
Sagiv, S., Reps, T.W., Wilhelm, R.: Parametric shape analysis via 3-valued logic. ACM Trans. Program. Lang. Syst. 24(3), 217–298 (2002)
Yorsh, G., Rabinovich, A.M., Sagiv, M., Meyer, A., Bouajjani, A.: A logic of reachable patterns in linked data-structures. J. Log. Algebr. Program. 73(1-2), 111–142 (2007)
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Bouajjani, A., Drăgoi, C., Enea, C., Sighireanu, M. (2009). A Logic-Based Framework for Reasoning about Composite Data Structures. In: Bravetti, M., Zavattaro, G. (eds) CONCUR 2009 - Concurrency Theory. CONCUR 2009. Lecture Notes in Computer Science, vol 5710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04081-8_13
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DOI: https://doi.org/10.1007/978-3-642-04081-8_13
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