Interval polyhedra: An abstract domain to infer interval linear relationships

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

Volumn 5673 LNCS, Issue , 2009, Pages 309-325

  Chen, Liqian ^a,b   Miné, Antoine ^b,c   Wang, Ji ^a   Cousot, Patrick ^b,d  

^a NATIONAL UNIVERSITY OF DEFENSE TECHNOLOGY   (China)

^b ECOLE NORMALE SUPÉRIEURE   (France)

^c CNRS   (France)

^d NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ABSTRACT DOMAINS; CONVEX POLYHEDRONS; FOURIER-MOTZKIN ELIMINATION; INTERVAL UNCERTAINTY; LINEAR CONSTRAINTS; LINEAR RELATIONSHIPS; NON-LINEAR; PROGRAM VARIABLES; UNCERTAIN INPUT DATA;

LINEARIZATION; STATIC ANALYSIS; SYNTHETIC APERTURE SONAR;

ABSTRACTING;

EID: 70350302846     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-03237-0_21     Document Type: Conference Paper

References (24)

1. APRON numerical abstract domain library, http://apron.cri.ensmp.fr/ library/
2. Allamigeon, X., Gaubert, S., Goubault, E.: Inferring min and max invariants using max-plus polyhedra. In: Alpuente, M., Vidal, G. (eds.) SAS 2008. LNCS, vol. 5079, pp. 189-204. Springer, Heidelberg (2008)
3. Bagnara, R., Hill, P.M., Zaffanella, E.:Widening operators for powerset domains. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 135-148. Springer, Heidelberg (2004)
4. Chen, L., Miné, A., Cousot, P.: A sound floating-point polyhedra abstract domain. In: Ramalingam, G. (ed.) APLAS 2008. LNCS, vol. 5356, pp. 3-18. Springer, Heidelberg (2008)
5. Chineck, J.W., Ramadan, K.: Linear programming with interval coefficients. Journal of the Operational Research Society 51(2), 209-220 (2000)
6. Cousot, P., Cousot, R.: Static determination of dynamic properties of programs. In: Proc. of the 2nd International Symposium on Programming, Dunod, Paris, pp. 106-130 (1976)
7. Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: ACM POPL 1977, pp. 238-252. ACM Press, New York (1977)
8. Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: ACM POPL 1979, pp. 269-282. ACM Press, New York (1979)
9. Cousot, P., Cousot, R.: Higher-order abstract interpretation (and application to comportment analysis generalizing strictness, termination, projection and PER analysis of functional languages). In: ICCL 1994, pp. 95-112. IEEE Computer Society Press, Los Alamitos (1994)
10. Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: ACM POPL 1978, pp. 84-96. ACM Press, New York (1978)
11. Giacobazzi, R., Ranzato, F.: Optimal domains for disjunctive abstract interpretation. Sci. Comput. Program 32(1-3), 177-210 (1998)
12. Granger, P.: Static analysis of arithmetical congruences. International Journal of Computer Mathematics 30, 165-199 (1989)
13. Gulavani, B.S., Gulwani, S.: A numerical abstract domain based on expression abstraction and max operator with application in timing analysis. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 370-384. Springer, Heidelberg (2008)
14. Jansson, C.: Calculation of exact bounds for the solution set of linear interval systems. Linear Algebra and Its Applications 251, 321-340 (1997)
15. Jansson, C.: Rigorous lower and upper bounds in linear programming. SIAM Journal on Optimization 14(3), 914-935 (2004)
16. Lalire, G., Argoud, M., Jeannet, B.: Interproc, http://pop-art.inrialpes. fr/people/bjeannet/bjeannet-forge/interproc/
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. Makhorin, A.: The GNU Linear Programming Kit (2000), http://www.gnu.org/ software/glpk/
19. Miné, A.: Relational abstract domains for the detection of floating-point run-time errors. In: Schmidt, D. (ed.) ESOP 2004. LNCS, vol. 2986, pp. 3-17. Springer, Heidelberg (2004)
20. Miné, A.: The octagon abstract domain. Higher-Order and Symbolic Computation 19(1), 31-100 (2006)
21. Miné, A.: Symbolic methods to enhance the precision of numerical abstract domains. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 348-363. Springer, Heidelberg (2005)
22. Oettli, W., Prager, W.: Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides. Numer. Math. 6, 405-409 (1964)
23. Rohn, J.: A handbook of results on interval linear problems. Technical report, Czech Academy of Sciences, Prague, Czech Republic (April 2005)
24. Rohn, J.: Solvability of systems of interval linear equations and inequalities. In: Linear Optimization Problems with Inexact Data, pp. 35-77. Springer, US (2006)