Automatic modular abstractions for linear constraints

ACM SIGPLAN Notices

Volumn 44, Issue 1, 2009, Pages 140-151

  Monniaux, David ^a  

^a VERIMAG   (France)

Author keywords

Abstract interpretation; Linear inequalities; Program transformation; Quantifier elimination

Indexed keywords

ABSTRACTING; DIGITAL ARITHMETIC; EMBEDDED SYSTEMS; LINEAR TRANSFORMATIONS; MATHEMATICAL TRANSFORMATIONS; MODEL CHECKING; RECURSIVE FUNCTIONS; STATIC ANALYSIS;

ABSTRACT INTERPRETATIONS; LINEAR ASSIGNMENT; LINEAR CONSTRAINTS; LINEAR INEQUALITIES; PROGRAM TRANSFORMATIONS; QUANTIFIER ELIMINATION; SYMBOLIC MANIPULATION; SYNCHRONOUS PROGRAMMING;

FUNCTIONAL PROGRAMMING;

EID: 70350339814     PISSN: 15232867     EISSN: None     Source Type: Journal    
DOI: 10.1145/1594834.1480899     Document Type: Conference Paper

References (49)

1. Roberto Bagnara, Patricia M. Hill, Elena Mazzi, and Enea Zaffanella. Widening operators for weakly-relational numeric abstractions. In Static Analysis (SAS), volume 3672 of LNCS, pages 3-18. Springer, 2005a. DOI: 10.1007/11547662-3.
2. Roberto Bagnara, Patricia M. Hill, Elisa Ricci, and Enea Zaffanella. Precise widening operators for convex polyhedra. Sci. Comput. Program., 58(1-2):28-56, 2005b. DOI: 10.1016/j.scico.2005.02.003.
3. Roberto Bagnara, Patricia M. Hill, and Enea Zaffanella. The Parma Polyhedra Library, version 0.9, 2006. URL http//www.cs.unipr.it/ppl.
4. Gogul Balakrishnan and Thomas Reps. Analyzing memory accesses in x86 executables. In Compiler Construction (CC), volume 2985 of LNCS, pages 5-23. Springer, 2004. DOI: 10.1007/b95956.
5. Bruno Blanchet, Patrick Cousot, Radhia Cousot, Jérôme Feret, Laurent Mauborgne, Antoine Miné, David Monniaux, and Xavier Rival. Design and implementation of a special-purpose static program analyzer for safety-critical real-time embedded software. In The Essence of Computation: Complexity, Analysis, Transformation, number 2566 in LNCS, pages 85-108. Springer, 2002. DOI: 10.1007/3-540-36377-7-5.
6. Bruno Blanchet, Patrick Cousot, Radhia Cousot, Jérôme Feret, Laurent Mauborgne, Antoine Miné, David Monniaux, and Xavier Rival. A static analyzer for large safety-critical software. In Programming Language Design and Implementation (PLDI), pages 196-207. ACM, 2003. DOI: 10.1145/781131.781153.
7. François Bourdoncle. Sémantique des langages impératifs d'ordre supérieur et interprétation abstraite. PhD thesis, École polytechnique, Palaiseau, 1992.
8. Aaron R. Bradley and Zohar Manna. The Calculus of Computation: Decision Procedures with Applications to Verification. Springer, October 2007.
9. Paul Caspi, Daniel Pilaud, Nicolas Halbwachs, and John A. Plaice. LUSTRE: a declarative language for real-time programming. In Principles of Programming Languages (POPL), pages 178-188. ACM, 1987. DOI: 10.1145/41625.41641.
10. Paul Caspi, Adrian Curic, Aude Maignan, Christos Sofronis, Stavros Tri-pakis, and Peter Niebert. From Simulink to Scade/Lustre to TTA: a layered approach for distributed embedded applications. SIGPLAN notices, 38(7): 153-162, 2003. DOI: 10.1145/780731.780754.
11. CAV05. Computer Aided Verification (CAV), number 4590 in LNCS, 2005. Springer. DOI: 10.1007/b138445.
12. Robert Clarisó and Jordi Cortadella. The octahedron abstract domain. In Static Analysis (SAS), number 3148 in LNCS, pages 312-327. Springer, 2004.
13. Michael Colon, Sriram Sankaranarayanan, and Henny Sipma. Linear invariant generation using non-linear constraint solving. In Computer Aided Verification (CAV), number 2725 in LNCS, pages 420-433. Springer, 2003.
14. Patrick Cousot. Proving program invariance and termination by parametric abstraction, lagrangian relaxation and semidefinite programming. In VMCAI05, pages 1-24. DOI: 10.1007/bl05073.
15. Patrick Cousot and Radhia Cousot. Abstract interpretation and application to logic programs. J. of Logic Programming, 13(2-3):103-179, 1992.
16. Patrick Cousot and Radhia Cousot. Static determination of dynamic properties of programs. In Proceedings of the Second International Symposium on Programming, pages 106-130. Dunod, Paris, France, 1976.
17. Patrick Cousot and Nicolas Halbwachs. Automatic discovery of linear restraints among variables of a program. In Principles of Programming Languages (POPL), pages 84-96. ACM, 1978. DOI: 10.1145/512760.512770.
18. Patrick Cousot, Radhia Cousot, Jérôme Feret, Laurent Mauborgne, Antoine Miné, David Monniaux, and Xavier Rival. The ASTRÉE analyzer. In Programming Languages and Systems (ESOP), number 3444 in LNCS, pages 21-30, 2005.
19. ESOP07. Programming Languages and Systems (ESOP), volume 4421 of LNCS, 2007. Springer. DOI: 10.1007/978-3-540-71316-6.
20. Jeanne Ferrante and Charles Rackoff. A decision procedure for the first order theory of real addition with order. SIAM Journal of Computation, 4(l):69-76, March 1975.
21. Michael J. Fischer and Michael O. Rabin. Super-exponential complexity of Presburger arithmetic. In Complexity of Computation, number 7 in SIAM-AMS proceedings, pages 27-42. American Mathematical Society, 1974.
22. Stéphane Gaubert, Eric Goubault, Ankur Taly, and Sarah Zennou. Static analysis by policy iteration on relational domains. In ESOP07, pages 237-252. DOI: 10.1007/978-3-540-71316-6.
23. Thomas Gawlitza and Helmut Seidl. Precise fixpoint computation through strategy iteration. In ESOP07, pages 300-315. DOI: 10.1007/978-3-540-71316-6-21.
24. Laure Gonnord and Nicolas Halbwachs. Combining widening and acceleration in linear relation analysis. In Static Analysis (SAS), volume 4134 of LNCS, pages 144-160. Springer, 2006. DOI: 10.1007/11823230.10.
25. Denis Gopan and Thomas W. Reps. Lookahead widening. In Computer Aided Verification (CAV), volume 4144 of LNCS, pages 452-466. Springer, 2006. DOI: 10.1007/11817963-41.
26. Denis Gopan and Thomas W. Reps. Low-level library analysis and summarization. In Computer Aided Verification (CAV), volume 4590 of LNCS, pages 68-81. Springer, 2007. DOI: 10.1007/978-3-540-73368-3-10.
27. Sumit Gulwani, Saurabh Srivastava, and Ramarathnam Venkatesan. Program analysis as constraint solving. In Programming Language Design and Implementation (PLDI). ACM, 2008. DOI: 10.1145/1375581.1375616.
28. Nicolas Halbwachs. Détermination automatique de relations linéaires vérifiées par les variables d'un programme. PhD thesis, Université scientifique et médicale de Grenoble, 1979.
29. IEEE standard for Binary floating-point arithmetic for microprocessor systems. IEEE 1985. ANSI/IEEE Std 754-1985.
30. Bertrand Jeannet. Dynamic partitioning in linear relation analysis, application to the verification of reactive systems. Formal Methods in System Design, 23(1):5-37, July 2003.
31. Deepak Kapur. Automatically generating loop invariants using quantifier elimination. In ACA (Applications of Computer Algebra), 2004.
32. Akash Lal, Gogul Balakrishnan, and Thomas Reps. Extended weighted pushdown systems. In CAV05, pages 343-357. DOI: 10.1007/11817963-32.
33. Francesco Logozzo and Manuel Fähndrich. On the relative completeness of bytecode analysis versus source code analysis. In Compiler Construction (CC), volume 4959 of LNCS, pages 197-212. Springer, 2008. DOI: 10.1007/978-3-540-78791-4-14.
34. Zohar Manna and John McCarthy. Properties of programs and partial function logic. In Machine Intelligence, 5, pages 27-38. Edinburgh University Press, 1969.
35. Zohar Manna and Amir Pnueli. Formalization of properties of functional programs. J. ACM, 17(3):555-569, 1970. DOI: 10.1145/321592.321606.
36. Florian Martin, Martin Alt, Reinhard Wilhelm, and Christian Ferdinand. Analysis of loops. In Compiler Construction (CC), volume 1383 of LNCS, pages 80-94. Springer, 1998.
37. Antoine Miné. The octagon abstract domain. In Reverse Engineering (WCRE), pages 310-319. IEEE, 2001. DOI: 10.1109AVCRE.2001.957836.
38. Antoine Miné. Relational abstract domains for the detection of floatingpoint run-time errors. In Programming Languages and Systems (ESOP), volume 2986 of LNCS, pages 3-17. Springer, 2004.
39. David Monniaux. Compositional analysis of floating-point linear numerical filters. In CAV05, pages 199-212. DOI: 10.1007/bl38445.
40. David Monniaux. A quantifier elimination algorithm for linear real arithmetic. In LPAR (Logic for Programming, Artificial Intelligence, and Reasoning), LNCS. Springer, 2008a.
41. David Monniaux. Optimal abstraction on real-valued programs. In Static analysis (SAS), number 4634 in LNCS, pages 104-120. Springer, 2007. DOI: 10.1007/978-3-540-74061-2-7.
42. David Monniaux. The pitfalls of verifying floating-point computations. ACM Transactions on programming languages and systems, 30(3): 12, 2008b. DOI: 10.1145/1353445.1353446. (Pubitemid 351724253)
43. George C. Necula, Scott McPeak, Shree P. Rahul, and Westley Weimer. CIL: Intermediate language and tools for analysis and transformation of C programs. In Compiler Construction (CC), volume 2304 of LNCS, pages 209-265. Springer, 2002. DOI: 10.1007/3-540-45937-5-16.
44. Radu Rugina and Martin Rinard. Symbolic bounds analysis for pointers, array indices, and accessed memory regions. ACM Trans. on Programming Languages and Systems (TOPLAS), 27(2): 185-235, 2005. DOI: 10.1145/349299.349325.
45. Sriram Sankaranarayanan, Henny Sipma, and Zohar Manna. Constraint-based linear-relations analysis. In SAS, number 3148 in LNCS, pages 53-68. Springer, 2004.
46. Sriram Sankaranarayanan, Henny Sipma, and Zohar Manna. Scalable analysis of linear systems using mathematical programming. In VMCAI05, pages 21-47. DOI: 10.1007/bl05073.
47. Helmut Seidl, Andrea Flexeder, and Michael Petter. Interprocedurally analysing linear inequality relations. In ESOP07, pages 284-299. DOI: 10.1007/978-3-540-71316-6-20.
48. Micha Sharir and Amir Pnueli. Two approaches to inter-procedural dataflow analysis. In Program Flow Analysis: Theory and Application. Prentice-Hall, 1981.
49. VMCAI05. Verification, Model Checking and Abstract Interpretation (VM-CAI), number 3385 in LNCS, 2005. Springer. DOI: 10.1007/bl05073.