A logical product approach to zonotope intersection

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6174 LNCS, Issue , 2010, Pages 212-226

  Ghorbal, Khalil ^a   Goubault, Eric ^a   Putot, Sylvie ^a  

^a DIF   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ABSTRACT DOMAINS; ABSTRACT INTERPRETATIONS; CONVEX DOMAINS; NON-LINEAR; REACHABILITY ANALYSIS; ZONOTOPES;

COMPUTER AIDED ANALYSIS; GEOMETRY; HYBRID SYSTEMS;

ABSTRACTING;

EID: 77954981309     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-14295-6_22     Document Type: Conference Paper

References (21)

1. Adje, A., Gaubert, S., Goubault, E.: Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis. In: Proceedings of European Symposium on Programming (to appear, 2010)
2. Allamigeon, X., Gaubert, S., Goubault, E.: Inferring Min and Max Invariants Using Maxplus Polyhedra. In: Alpuente, M., Vidal, G. (eds.) SAS 2008. LNCS, vol. 5079, pp. 189-204. Springer, Heidelberg (2008)
3. Bouissou, O., Conquet, E., Cousot, P., Cousot, R., Feret, J., Ghorbal, K., Goubault, E., Lesens, D., Mauborgne, L., Mine, A., Putot, S., Rival, X.: Space software validation using abstract interpretation. In: Proceedings of the Int. Space System Engineering Conference, Data Systems in Aerospace DASIA'09 (2009)
4. Comba, J.L.D., Stolfi, J.: Affine arithmetic and its applications to computer graphics. In: Proceedings of SIBGRAPI (1993)
5. Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: Proceedings of Principles Of Programming Languages, pp. 269-282. ACM Press, New York (1979)
6. Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: Proceedings of Principles of Programming Languages, pp. 84-96. ACMPress, New York (1978)
7. Ghorbal, K.,Goubault, E., Putot, S.: The zonotope abstract domain Taylor1+. In: Bouajjani, A.,Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 627-633. Springer, Heidelberg (2009)
8. Girard, A.: Reachability of uncertain linear systems using zonotopes. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 291-305. Springer, Heidelberg (2005)
9. Girard, A., Le Guernic, C.: Zonotope/hyperplane intersection for hybrid systems reachability analysis. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 215-228. Springer, Heidelberg (2008)
10. Goubault, E., Putot, S.: Weakly relational domains for floating-point computation analysis. Presented at the second international workshop on Numerical and Symbolic Abstract Domains (2005), http://www.di.ens.fr/~goubault/ papers/NSAD05.pdf
11. Goubault, E., Putot, S.: Static analysis of numerical algorithms. In: Yi, K. (ed.) SAS 2006. LNCS, vol. 4134, pp. 18-34. Springer, Heidelberg (2006)
12. Goubault, E., Putot, S.: Under-approximations of computations in real numbers based on generalized affine arithmetic. In: Riis Nielson, H., Filé, G. (eds.) SAS 2007. LNCS, vol. 4634, pp. 137-152. Springer, Heidelberg (2007)
13. Goubault, E., Putot, S.: Perturbed affine arithmetic for invariant computation in numerical program analysis. In: CoRR, abs/0807.2961 (2008), http://arxiv.org/abs/0807.2961
14. Goubault, E., Putot, S.: A zonotopic framework for functional abstractions. In: CoRR, abs/0910.1763 (2009), http://arxiv.org/abs/0910.1763
15. Gulwani, S., Tiwari, A.: Combining abstract interpreters. In: Proceedings of the ACM SIGPLAN conference on Programming language design and implementation, pp. 376-386. ACM Press, New York (2006)
16. Keil, C.: Lurupa - rigorous error bounds in linear programming. In: Algebraic and Numerical Algorithms and Computer-assisted Proofs, Dagstuhl Seminar 5391 (2005)
17. Laviron, V., Logozzo, F.: Subpolyhedra: A (more) scalable approach to infer linear inequalities. In: Jones, N.D.,Müller-Olm, M. (eds.) VMCAI 2009. LNCS, vol. 5403, pp. 229-244. Springer, Heidelberg (2009)
18. Manna, Z., Bradley, A.R.: The Calculus of Computation; Decision procedures with applications to verification. Springer, Heidelberg (2007)
19. Miné, A.: A new numerical abstract domain based on difference-bound matrices. In: Danvy, O., Filinski, A. (eds.) PADO 2001. LNCS, vol. 2053, pp. 155-172. Springer, Heidelberg (2001)
20. APRON Project. Numerical abstract domain library (2007), http://apron.cri.ensmp.fr
21. Sankaranarayanan, S., Sipma, H.B., Manna, Z.: Scalable analysis of linear systems using mathematical programming. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 25-41. Springer, Heidelberg (2005)