Abstract
Computer Games Software deeply relies on physics simulations, which are particularly demanding to analyze because they manipulate a large amount of interleaving floating point variables. Therefore, this application domain is an interesting workbench to stress the trade-off between accuracy and efficiency of abstract domains for static analysis.
In this paper, we introduce Parametric Hypercubes, a novel disjunctive non-relational abstract domain. Its main features are: (i) it combines the low computational cost of operations on (selected) multidimensional intervals with the accuracy provided by lifting to a power-set disjunctive domain, (ii) the compact representation of its elements allows to limit the space complexity of the analysis, and (iii) the parametric nature of the domain provides a way to tune the accuracy/efficiency of the analysis by just setting the widths of the hypercubes sides.
The first experimental results on a representative Computer Games case study outline both the efficiency and the precision of the proposal.
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References
Alur, R., Dang, T., Ivančić, F.: Reachability analysis of hybrid systems via predicate abstraction. In: Tomlin, C.J., Greenstreet, M.R. (eds.) HSCC 2002. LNCS, vol. 2289, pp. 35–48. Springer, Heidelberg (2002)
Alur, R., Henzinger, T.A., Lafferriere, G., Pappas, G.J.: Discrete abstractions of hybrid systems. Proceedings of the IEEE 88(7), 971–984 (2000)
Amato, G., Scozzari, F.: The abstract domain of parallelotopes. Electronic Notes Theoretical Computer Science 287, 17–28 (2012)
Bagnara, R., Hill, P.M., Zaffanella, E.: Widening operators for powerset domains. In: STTT, vol. 9(3-4), pp. 413–414 (2007)
Bouissou, O.: Proving the correctness of the implementation of a control-command algorithm. In: Palsberg, J., Su, Z. (eds.) SAS 2009. LNCS, vol. 5673, pp. 102–119. Springer, Heidelberg (2009)
Bouissou, O.: From control-command synchronous programs to hybrid automata. In: ADHS 2012 (June 2012)
Bouissou, O., Mimram, S., Chapoutot, A.: Hyson: Set-based simulation of hybrid systems. In: RSP 2012, pp. 79–85 (2012)
Clarke, E.M., 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)
Costantini, G., Ferrara, P., Cortesi, A.: Linear approximation of continuous systems with trapezoid step functions. In: Jhala, R., Igarashi, A. (eds.) APLAS 2012. LNCS, vol. 7705, pp. 98–114. Springer, Heidelberg (2012)
Cousot, P.: The calculational design of a generic abstract interpreter. In: Calculational System Design. NATO ASI Series F. IOS Press, Amsterdam (1999)
Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: Proceedings of POPL 1978. ACM Press (1978)
Eberly, D.H.: Game Physics. Interactive 3D technology series. Elsevier Science (2010)
Filé, G., Ranzato, F.: The powerset operator on abstract interpretations. Theor. Comput. Sci. 222(1-2), 77–111 (1999)
Ghorbal, K., Ivančić, F., Balakrishnan, G., Maeda, N., Gupta, A.: Donut domains: Efficient non-convex domains for abstract interpretation. In: Kuncak, V., Rybalchenko, A. (eds.) VMCAI 2012. LNCS, vol. 7148, pp. 235–250. Springer, Heidelberg (2012)
Gurfinkel, A., Chaki, S.: Boxes: A symbolic abstract domain of boxes. In: Cousot, R., Martel, M. (eds.) SAS 2010. LNCS, vol. 6337, pp. 287–303. Springer, Heidelberg (2010)
Halbwachs, N., Merchat, D., Gonnord, L.: Some ways to reduce the space dimension in polyhedra computations. Formal Methods in System Design 29(1), 79–95 (2006)
Halbwachs, N., Raymond, P., Proy, Y.-E.: Verification of linear hybrid systems by means of convex approximations. In: LeCharlier, B. (ed.) SAS 1994. LNCS, vol. 864, pp. 223–237. Springer, Heidelberg (1994)
Howe, J.M., King, A., Lawrence-Jones, C.: Quadtrees as an abstract domain. Electronic Notes in Theoretical Computer Science 267(1), 89–100 (2010)
Mauborgne, L., Rival, X.: Trace partitioning in abstract interpretation based static analyzers. In: Sagiv, M. (ed.) ESOP 2005. LNCS, vol. 3444, pp. 5–20. Springer, Heidelberg (2005)
Miné, A.: The octagon abstract domain. In: Higher-Order and Symbolic Computation (2006)
Ratschan, S., She, Z.: Safety verification of hybrid systems by constraint propagation based abstraction refinement. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 573–589. Springer, Heidelberg (2005)
Sankaranarayanan, S., Ivančić, F., Shlyakhter, I., Gupta, A.: Static analysis in disjunctive numerical domains. In: Yi, K. (ed.) SAS 2006. LNCS, vol. 4134, pp. 3–17. Springer, Heidelberg (2006)
Seladji, Y., Bouissou, O.: Fixpoint computation in the polyhedra abstract domain using convex and numerical analysis tools. In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 149–168. Springer, Heidelberg (2013)
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Costantini, G., Ferrara, P., Maggiore, G., Cortesi, A. (2013). The Domain of Parametric Hypercubes for Static Analysis of Computer Games Software. In: Groves, L., Sun, J. (eds) Formal Methods and Software Engineering. ICFEM 2013. Lecture Notes in Computer Science, vol 8144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41202-8_29
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DOI: https://doi.org/10.1007/978-3-642-41202-8_29
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