A method for symbolic computation of abstract operations

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

Volumn 7358 LNCS, Issue , 2012, Pages 174-192

  Thakur, Aditya ^a   Reps, Thomas ^a,b  

^a University of Wisconsin Madison   (United States)

^b GRAMMATECH INC   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ABSTRACT DOMAINS; ABSTRACT INTERPRETATIONS; PROGRAM ANALYSIS; PROGRAM SEMANTICS; SATISFIABILITY MODULO THEORIES; SYMBOLIC COMPUTATION;

APPROXIMATION ALGORITHMS; COMPUTER AIDED ANALYSIS; SEMANTICS;

ABSTRACTING;

EID: 84864053250     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-31424-7_17     Document Type: Conference Paper

References (37)

1. Armando, A., Castellini, C., Giunchiglia, E.: SAT-Based Procedures for Temporal Reasoning. In: Biundo, S., Fox, M. (eds.) ECP 1999. LNCS, vol. 1809, pp. 97-108. Springer, Heidelberg (2000)
2. Ball, T., Podelski, A., Rajamani, S.K.: Boolean and Cartesian Abstraction for Model Checking C Programs. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 268-283. Springer, Heidelberg (2001)
3. Björk, M.: First order Stålmarck. J. Autom. Reasoning 42(1), 99-122 (2009)
4. Bjørner, N., de Moura, L.: Accelerated lemma learning using joins-DPLL(∐). In: LPAR (2008)
5. Bryant, R.E., Velev, M.N.: Boolean satisfiability with transitivity constraints. Trans. on Computational Logic 3(4) (2002)
6. Clarke, E., Kroening, D., Sharygina, N., Yorav, K.: Predicate abstraction of ANSIC programs using SAT. FMSD 25(2-3) (2004)
7. Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: POPL (1979)
8. Cousot, P., Halbwachs, N.: Automatic discovery of linear constraints among variables of a program. In: POPL (1978)
9. Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Commun. ACM 5(7) (1962)
10. Davis, M., Putnam, H.: A computing procedure for quantification theory. J. ACM 7(3) (1960)
11. 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)
12. Elder, M., Lim, J., Sharma, T., Andersen, T., Reps, T.: Abstract Domains of Affine Relations. In: Yahav, E. (ed.) SAS 2011. LNCS, vol. 6887, pp. 198-215. Springer, Heidelberg (2011)
13. Flanagan, C., Joshi, R., Ou, X., Saxe, J.B.: Theorem Proving Using Lazy Proof Explication. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 355-367. Springer, Heidelberg (2003)
14. Graf, S., Saïdi, H.: Construction of Abstract State Graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72-83. Springer, Heidelberg (1997)
15. Graham, S.,Wegman, M.: A fast and usually linear algorithm for data flow analysis. J. ACM 23(1), 172-202 (1976)
16. Granger, P.: Improving the Results of Static Analyses Programs by Local Decreasing Iteration. In: Shyamasundar, R.K. (ed.) FSTTCS 1992. LNCS, vol. 652, pp. 68-79. Springer, Heidelberg (1992)
17. Gulwani, S., Musuvathi,M.: Cover Algorithms and Their Combination. In: Gairing, M. (ed.) ESOP 2008. LNCS, vol. 4960, pp. 193-207. Springer, Heidelberg (2008)
18. Harrison, J.: Stålmarck's Algorithm as a HOL Derived Rule. In: von Wright, J., Harrison, J., Grundy, J. (eds.) TPHOLs 1996. LNCS, vol. 1125, pp. 221-234. Springer, Heidelberg (1996)
19. Karr, M.: Affine relationship among variables of a program. Acta Inf. 6 (1976)
20. Kidd, N., Lal, A., Reps, T.: WALi: The Weighted Automaton Library (2007), www.cs.wisc.edu/wpis/wpds/download.php
21. King, A., Søndergaard, H.: Automatic Abstraction for Congruences. In: Barthe, G., Hermenegildo, M. (eds.) VMCAI 2010. LNCS, vol. 5944, pp. 197-213. Springer, Heidelberg (2010)
22. Knoop, J., Steffen, B.: Interprocedural Coincidence Theorem. In: Pfahler, P., Kastens, U. (eds.) CC 1992. LNCS, vol. 641, pp. 125-140. Springer, Heidelberg (1992)
23. Lal, A., Reps, T.: Improving Pushdown SystemModel Checking. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 343-357. Springer, Heidelberg (2006)
24. Lal, A., Reps, T., Balakrishnan, G.: Extended Weighted Pushdown Systems. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 434-448. Springer, Heidelberg (2005)
25. McMillan, K.L., Kuehlmann, A., Sagiv, M.: Generalizing DPLL to Richer Logics. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 462-476. Springer, Heidelberg (2009)
26. Monniaux, D.: Automatic modular abstractions for template numerical constraints. LMCS 6(3) (2010)
27. Müller-Olm, M., Seidl, H.: Analysis of modular arithmetic. TOPLAS (2007)
28. PPL: The Parma polyhedra library, http://www.cs.unipr.it/ppl/
29. Reps, T., Sagiv, M., Yorsh, G.: Symbolic Implementation of the Best Transformer. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 252-266. Springer, Heidelberg (2004)
30. Sagiv, M., Reps, T., Wilhelm, R.: Parametric shape analysis via 3-valued logic. TOPLAS 24(3), 217-298 (2002)
31. 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)
32. Sharir, M., Pnueli, A.: Two approaches to interprocedural data flow analysis. In: Program Flow Analysis: Theory and Applications. Prentice-Hall (1981)
33. Sheeran, M., Stålmarck, G.: A tutorial on Stålmarck's proof procedure for propositional logic. FMSD 16(1) (2000)
34. Strichman, O.: On Solving Presburger and Linear Arithmetic with SAT. In: Aagaard, M.D., O'Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, pp. 160-170. Springer, Heidelberg (2002)
35. Thakur, A., Reps, T.: A generalization of Stålmarck's method. TR 1699. CS Dept., Univ. of Wisconsin, Madison, WI (October 2011)
36. Thakur, A., Reps, T.: A method for symbolic computation of precise abstract operations. TR 1708. CS Dept., Univ. of Wisconsin, Madison, WI (January 2012)
37. Yorsh, G., Reps, T., Sagiv, M.: Symbolically Computing Most-Precise Abstract Operations for Shape Analysis. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 530-545. Springer, Heidelberg (2004)