SubPolyhedra: A family of numerical abstract domains for the (more) scalable inference of linear inequalities

International Journal on Software Tools for Technology Transfer

Volumn 13, Issue 6, 2011, Pages 585-601

  Laviron, Vincent ^a   Logozzo, Francesco ^b  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b MICROSOFT RESEARCH   (United States)

Author keywords

Abstract domains; Abstract interpretation; Loop invariants; Numerical abstract domains; Static analysis

Indexed keywords

ABSTRACT DOMAINS; ABSTRACT INTERPRETATIONS; COMPLEX CODES; JOIN POINT; LINEAR EQUALITY; LINEAR INEQUALITIES; LOOP INVARIANTS; SCALABLE ANALYSIS;

GEOMETRY; STATIC ANALYSIS;

ABSTRACTING;

EID: 80053312057     PISSN: 14332779     EISSN: 14332787     Source Type: Journal    
DOI: 10.1007/s10009-011-0199-5     Document Type: Article

References (37)

1. Bagnara, R., Hill, P. M., Zaffanella, E.: The Parma Polyhedra Library. http://www. cs. unipr. it/ppl/ (2011).
2. Barnett, M., Fähndrich, M. A., Logozzo, F.: Foxtrot and Clousot: Language Agnostic Dynamic and Static Contract Checking for. Technical Report MSR-TR-2008-105. Microsoft Research (2008).
3. Barnett, M., Fändrich, M., Garbervetsky, D., Logozzo, F.: Annotations for (more) precise points-to analysis. In: IWACO 2007 (July 2007).
4. Blanchet, B., Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Monniaux, D., Rival, X.: A static analyzer for large safety-critical software. In: PLDI'03. ACM Press, New York (2003).
5. Chang, B.-Y. E., Leino, K. R. M.: Abstract interpretation with alien expressions and heap structures. In: VMCAI'05. Springer, Berlin (2005).
6. Chvátal V.: Linear Programming. W. H. Freeman, New York (1983).
7. Clarisó, R., Cortadella, J.: The octahedron abstract domain. In: SAS'04 (2004).
8. Cousot, P.: The calculational design of a generic abstract interpreter. In: Calculational System Design. NATO ASI Series F. IOS Press, Amsterdam (1999).
9. Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL'77 (1977).
10. Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: POPL'79 (1979).
11. Cousot P., Cousot R.: Abstract interpretation and application to logic programs. J. Logic Program. 13(2-3), 103-179 (1992).
12. Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Monniaux, D., Rival, X.: Combination of abstractions in the ASTRÉE static analyzer. In: ASIAN'06. LNCS, vol. 4435, pp. 272-300. Springer, Berlin (2006).
13. Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: POPL'78 (1978).
14. Dantzig, G. B.: Programming in Linear Structures. Technical Report. USAF (1948).
15. Ferrara, P., Logozzo, F., Fähndrich, M. A.: Safer unsafe code in. Net. In: OOPSLA'08 (2008).
16. Granger, P.: Improving the results of static analyses programs by local decreasing iteration. In: FSTTCS'92. Springer, Berlin (1992).
17. Gulavani, B. S., Chakraborty, S., Nori, A. V., Rajamani, S. K.: Automatically refining abstract interpretations. In: TACAS'08 (2008).
18. Gulwani, S., McCloskey, B., Tiwari, A.: Lifting abstract interpreters to quantified logical domains. In: POPL'08. ACM Press, New York (2008).
19. Gulwani, S., Srivastava, S., Venkatesan, R.: Program analysis as constraint solving. In: PLDI'08 (2008).
20. Karr M.: On affine relationships among variables of a program. Acta Inform. 6(2), 133-151 (1976).
21. Khachiyan, L., Boros, E., Borys, K., Elbassioni, K. M., Gurvich, M.: Generating all vertices of a polyhedron is hard. In: SODA'06 (2006).
22. Kovács, L.: Reasoning algebraically about p-solvable loops. In: TACAS'08. Springer, Berlin (2008).
23. Laviron, V., Logozzo, F.: Refining abstract interpretation-based static analyses with hints. In: APLAS'09 (2009).
24. Laviron, V., Logozzo, F.: Subpolyhedra: a (more) scalable approach to infer linear inequalities. In: VMCAI'09 (2009).
25. Logozzo, F.: Cibai: an abstract interpretation-based static analyzer for modular analysis and verification of Java classes. In: VMCAI'07 (2007).
26. Logozzo, F., Fähndrich, M. A.: On the relative completeness of bytecode analysis versus source code analysis. In: CC'08 (2008).
27. Logozzo, F., Fähndrich, M. A.: Pentagons: A weakly relational abstract domain for the efficient validation of array accesses. In: SAC'08 (2008).
28. Meyer B.: Object-Oriented Software Construction, 2nd ed., Professional Technical Reference. Prentice Hall, Upper Saddle River (1997).
29. Miné, A.: The octagon abstract domain. In: WCRE 2001 (2001).
30. Miné, A.: Weakly Relational Numerical Abstract Domains. PhD Thesis. École Polythechnique (2004).
31. Müller-Olm, M., Seidl, H.: Precise interprocedural analysis through linear algebra. In: POPL'04 (2004).
32. Rodríguez-Carbonell E., Kapur D.: Automatic generation of polynomial invariants of bounded degree using abstract interpretation. Sci. Comput. Program. 64(1), 54-75 (2007).
33. Sankaranarayanan, S., Ivancic, F., Gupta A.: Program analysis using symbolic ranges. In: SAS'07 (2007).
34. Sankaranarayanan, S., Sipma, H. B., Manna, Z.: Scalable analysis of linear systems using mathematical programming. In: VMCAI'05 (2005).
35. Simon A.: Value-Range Analysis of C Programs. Springer, New York (2008).
36. Simon, A., King, A., Howe, J.: Two variables per linear inequality as an abstract domain. In: LOPSTR'02 (2002).
37. Spielman D. A., Teng S.-H.: Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time. J. ACM 51(3), 385-463 (2004).