Verification as learning geometric concepts

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

Volumn 7935 LNCS, Issue , 2013, Pages 388-411

  Sharma, Rahul ^a   Gupta, Saurabh ^b   Hariharan, Bharath ^b   Aiken, Alex ^a   Nori, Aditya V ^c  

^a STANFORD UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c MICROSOFT RESEARCH   (United States)

Author keywords

loop invariants; machine learning; verification

Indexed keywords

BOOLEAN COMBINATIONS; GEOMETRIC CONCEPTS; HOARE LOGIC; LEARNING PROBLEM; LOOP INVARIANTS; POLYNOMIAL INEQUALITIES; PROGRAM VERIFICATION; SAFETY PROPERTY;

FORMAL LOGIC; LEARNING ALGORITHMS; LEARNING SYSTEMS; VERIFICATION;

STATIC ANALYSIS;

EID: 84884477397     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-38856-9_21     Document Type: Conference Paper

References (56)

1. Albarghouthi, A., Gurfinkel, A., Chechik, M.: Craig interpretation. In: Miné, A., Schmidt, D. (eds.) SAS 2012. LNCS, vol. 7460, pp. 300-316. Springer, Heidelberg (2012)
2. Amato, G., Parton, M., Scozzari, F.: Discovering invariants via simple component analysis. J. Symb. Comput. 47(12), 1533-1560 (2012)
3. Bagnara, R., Hill, P.M., Zaffanella, E.: Widening operators for powerset domains. STTT 9(3-4) (2007)
4. Bagnara, R., Rodríguez-Carbonell, E., Zaffanella, E.: Generation of basic semi-algebraic invariants using convex polyhedra. In: Hankin, C., Siveroni, I. (eds.) SAS 2005. LNCS, vol. 3672, pp. 19-34. Springer, Heidelberg (2005)
5. Ball, T., Hackett, B., Lahiri, S.K., Qadeer, S., Vanegue, J.: Towards scalable modular checking of user-defined properties. In: Leavens, G.T., O'Hearn, P., Rajamani, S.K. (eds.) VSTTE 2010. LNCS, vol. 6217, pp. 1-24. Springer, Heidelberg (2010)
6. Ball, T., Rajamani, S.K.: The SLAM toolkit. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 260-264. Springer, Heidelberg (2001)
7. Barnett, M., Chang, B.-Y.E., DeLine, R., Jacobs, B., M. Leino, K.R.: Boogie: A modular reusable verifier for object-oriented programs. In: de Boer, F.S., Bonsangue, M.M., Graf, S., de Roever, W.-P. (eds.) FMCO 2005. LNCS, vol. 4111, pp. 364-387. Springer, Heidelberg (2006) (Pubitemid 44548955)
8. Berger, B., Rompel, J., Shor, P.W.: Efficient NC algorithms for set cover with applications to learning and geometry. J. Comput. Syst. Sci. 49(3), 454-477 (1994)
9. Beyer, D., Henzinger, T.A., Jhala, R., Majumdar, R.: The software model checker BLAST. STTT 9(5-6), 505-525 (2007)
10. Beyer, D., Henzinger, T.A., Majumdar, R., Rybalchenko, A.: Path invariants. In: PLDI, pp. 300-309 (2007)
11. Blumer, A., Ehrenfeucht, A., Haussler, D., Warmuth, M.K.: Learnability and the Vapnik-Chervonenkis dimension. JACM 36(4), 929-965 (1989)
12. Brönnimann, H., Goodrich, M.T.: Almost optimal set covers in finite VC-dimension. In: SoCG, pp. 293-302 (1994)
13. Bshouty, N.H., Goldman, S.A., Mathias, H.D., Suri, S., Tamaki, H.: Noise-tolerant distribution-free learning of general geometric concepts. In: STOC, pp. 151-160 (1996)
14. Cachera, D., Jensen, T., Jobin, A., Kirchner, F.: Inference of polynomial invariants for imperative programs: A farewell to gröbner bases. In: Miné, A., Schmidt, D. (eds.) SAS 2012. LNCS, vol. 7460, pp. 58-74. Springer, Heidelberg (2012)
15. Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233-235 (1979)
16. Clarisó, R., Cortadella, J.: The octahedron abstract domain. In: Giacobazzi, R. (ed.) SAS 2004. LNCS, vol. 3148, pp. 312-327. Springer, Heidelberg (2004)
17. Colón, M.A.: Approximating the algebraic relational semantics of imperative programs. In: Giacobazzi, R. (ed.) SAS 2004. LNCS, vol. 3148, pp. 296-311. Springer, Heidelberg (2004)
18. Colón, M.A., Sankaranarayanan, S.: Generalizing the template polyhedral domain. In: Barthe, G. (ed.) ESOP 2011. LNCS, vol. 6602, pp. 176-195. Springer, Heidelberg (2011)
19. Colon, M.A., Sankaranarayanan, S., Sipma, H.B.: Linear invariant generation using non-linear constraint solving. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 420-432. Springer, Heidelberg (2003)
20. Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273-297 (1995)
21. Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL, pp. 238-252 (1977)
22. Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: POPL, pp. 269-282 (1979)
23. Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: POPL, pp. 84-96 (1978)
24. Ernst, M.D., Perkins, J.H., Guo, P.J., McCamant, S., Pacheco, C., Tschantz, M.S., Xiao, C.: The Daikon system for dynamic detection of likely invariants. Sci. Comput. Program. 69(1-3), 35-45 (2007)
25. Fähndrich, M., Logozzo, F.: Static contract checking with abstract interpretation. In: Beckert, B., Marché, C. (eds.) FoVeOOS 2010. LNCS, vol. 6528, pp. 10-30. Springer, Heidelberg (2011)
26. Filé, G., Ranzato, F.: Improving abstract interpretations by systematic lifting to the powerset. In: GULP-PRODE, vol. (1), pp. 357-371 (1994)
27. Flanagan, C., Leino, K.R.M.: Houdini, an annotation assistant for ESC/Java. In: Oliveira, J.N., Zave, P. (eds.) FME 2001. LNCS, vol. 2021, pp. 500-517. Springer, Heidelberg (2001)
28. 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)
29. Gopan, D., Reps, T.: Guided static analysis. In: Riis Nielson, H., Filé, G. (eds.) SAS 2007. LNCS, vol. 4634, pp. 349-365. Springer, Heidelberg (2007)
30. Gulavani, B.S., Chakraborty, S., Nori, A.V., Rajamani, S.K.: Automatically refining abstract interpretations. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 443-458. Springer, Heidelberg (2008)
31. Gulavani, B.S., Henzinger, T.A., Kannan, Y., Nori, A.V., Rajamani, S.K.: Synergy: a new algorithm for property checking. In: FSE 2006, pp. 117-127 (2006)
32. Gulwani, S., Jojic, N.: Program verification as probabilistic inference. In: POPL, pp. 277-289 (2007)
33. Gulwani, S., Necula, G.C.: Discovering affine equalities using random interpretation. In: POPL, pp. 74-84 (2003)
34. Gulwani, S., Srivastava, S., Venkatesan, R.: Program analysis as constraint solving. In: PLDI, pp. 281-292 (2008)
35. Gupta, A., Majumdar, R., Rybalchenko, A.: From tests to proofs. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 262-276. Springer, Heidelberg (2009)
36. Ivancic, F., Sankaranarayanan, S.: NECLA Static Analysis Benchmarks, http://www.nec-labs.com/research/system/systems SAV-website/small static bench-v1.1.tar.gz
37. Jhala, R., McMillan, K.L.: A practical and complete approach to predicate refinement. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 459-473. Springer, Heidelberg (2006) (Pubitemid 44019391)
38. Kovács, L.: A complete invariant generation approach for p-solvable loops. In: Pnueli, A., Virbitskaite, I., Voronkov, A. (eds.) PSI 2009. LNCS, vol. 5947, pp. 242-256. Springer, Heidelberg (2010)
39. Lahiri, S.K., Qadeer, S.: Complexity and algorithms for monomial and clausal predicate abstraction. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 214-229. Springer, Heidelberg (2009)
40. Lalire, G., Argoud, M., Jeannet, B.: The Interproc Analyzer, http://pop-art.inrialpes.fr/people/bjeannet/bjeannet-forge/interproc/index.html
41. Laviron, V., Logozzo, F.: Subpolyhedra: a family of numerical abstract domains for the (more) scalable inference of linear inequalities. STTT 13(6), 585-601 (2011)
42. Lee, D., Yannakakis, M.: Online minimization of transition systems (extended abstract). In: STOC, pp. 264-274 (1992)
43. 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) (Pubitemid 41274047)
44. McCluskey, E.J.: Minimization of boolean functions. Bell Systems Technical Journal 35(6), 1417-1444 (1956)
45. de Moura, L., Bjørner, N.: Z3: An efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337-340. Springer, Heidelberg (2008)
46. Müller-Olm, M., Seidl, H.: Computing polynomial program invariants. Information Processing Letters 91(5), 233-244 (2004)
47. Naik, M., Yang, H., Castelnuovo, G., Sagiv, M.: Abstractions from tests. In: POPL, pp. 373-386 (2012)
48. Nguyen, T., Kapur, D.,Weimer,W., Forrest, S.: Using dynamic analysis to discover polynomial and array invariants. In: ICSE (2012)
49. Nimmer, J.W., Ernst, M.D.: Automatic generation of program specifications. In: ISSTA, pp. 229-239 (2002)
50. Rodríguez-Carbonell, E., Kapur, D.: Automatic generation of polynomial invariants of bounded degree using abstract interpretation. Sci. Comput. Program. 64(1), 54-75 (2007)
51. Rodríguez-Carbonell, E., Kapur, D.: Generating all polynomial invariants in simple loops. J. Symb. Comput. 42(4), 443-476 (2007)
52. Sankaranarayanan, S., Ivančíc, 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) (Pubitemid 44561963)
53. Sankaranarayanan, S., Sipma, H., Manna, Z.: Non-linear loop invariant generation using Gröbner bases. In: POPL, pp. 318-329 (2004)
54. Sharma, R., Gupta, S., Hariharan, B., Aiken, A., Liang, P., Nori, A.V.: A data driven approach for algebraic loop invariants. In: Felleisen, M., Gardner, P. (eds.) ESOP. LNCS, vol. 7792, pp. 574-592. Springer, Heidelberg (2013)
55. Sharma, R., Nori, A.V., Aiken, A.: Interpolants as classifiers. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 71-87. Springer, Heidelberg (2012)
56. Valiant, L.G.: A theory of the learnable. Commun. ACM 27(11), 1134-1142 (1984)