Efficient craig interpolation for linear diophantine (dis)equations and linear modular equations

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

Volumn 5123 LNCS, Issue , 2008, Pages 254-267

  Jain, Himanshu ^a   Clarke, Edmund ^a   Grumberg, Orna ^b  

^a Carnegie Mellon University

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER AIDED ANALYSIS; DIGITAL ARITHMETIC; INTERPOLATION; MODEL CHECKING; POLYNOMIAL APPROXIMATION;

COMPUTER AIDED VERIFICATION; COUNTEREXAMPLE-GUIDED ABSTRACTION REFINEMENT; CRAIG INTERPOLANTS; CRAIG INTERPOLATION; DIOPHANTINE EQUATIONS; EFFICIENT ALGORITHMS; HARDWARE AND SOFTWARE; INTERNATIONAL CONFERENCES; INTERPOLANTS; INTERPOLATION ALGORITHMS; LINEAR ARITHMETIC; LINEAR CONGRUENCES; MODEL CHECKERS; POLYNOMIAL-TIME ALGORITHMS;

LINEAR EQUATIONS;

EID: 48949095821     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-70545-1_24     Document Type: Conference Paper

References (21)

1. SATABS 1.9 website, http://www.verify.ethz.ch/satabs/
2. VCEGAR 1.3 website, http://www.cs.cmu.edu/~modelcheck/vcegar/
3. Yices 1.0.11 website, http://yices.csl.sri.com/
4. PARI/GP, Version 2.3.2 (2006), http://pari.math.u-bordeaux.fr/
5. Bockmayr, A., Weispfenning, V.: Solving numerical constraints. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 751-842 (2001)
6. Cimatti, A., Griggio, A., Sebastiani, R.: Efficient interpolation in satisfiability modulo theories. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 367-381. Springer, Heidelberg (2008)
7. Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement for symbolic model checking. J. ACM 50(5) (2003)
8. Craig, W.: Linear reasoning. a new form of the herbrand-gentzen theorem. J. Symb. Log. 22(3), 250-268 (1957)
9. Henzinger, T.A., Jhala, R., Majumdar, R., McMillan, K.L.: Abstractions from proofs. In: POPL, pp. 232-244. ACM Press, New York (2004)
10. Jain, H., Clarke, E.M., Grumberg, O.: Efficient craig interpolation for linear diophantine (dis)equations and linear modular equations. Technical Report CMU-CS-08-102, Carnegie Mellon University, School of Computer Science (2008)
11. Jhala, R., McMillan, K.L.: A Practical and Complete Approach to Predicate Refinement. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006 and ETAPS 2006. LNCS, vol. 3920, pp. 459-473. Springer, Heidelberg (2006)
12. Kapur, D., Majumdar, R., Zarba, C.G.: Interpolation for data structures. In: SIGSOFT 2006/FSE-14, pp. 105-116. ACM, New York (2006)
13. Kroening, D., Weissenbacher, G.: Lifting propositional interpolants to the word-level. In: FMCAD, pp. 85-89. IEEE, Los Alamitos (2007)
14. McMillan, K.L.: Interpolation and sat-based model checking. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 1-13. Springer, Heidelberg (2003)
15. McMillan, K.L.: An Interpolating Theorem Prover. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 16-30. Springer, Heidelberg (2004)
16. Müller-Olm, M., Seidl, H.: Analysis of modular arithmetic. ACM Trans. Program. Lang. Syst. 29(5), 29 (2007)
17. Nelson, G., Oppen, D.C.: Simplification by cooperating decision procedures. ACM Trans. Program. Lang. Syst. 1(2), 245-257 (1979)
18. Pudlák, P.: Lower bounds for resolution and cutting plane proofs and monotone computations. J. Symb. Log. 62(3), 981-998 (1997)
19. Rybalchenko, A., Sofronie-Stokkermans, V.: Constraint solving for interpolation. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 346-362. Springer, Heidelberg (2007)
20. Schrijver, A.: Theory of linear and integer programming. John Wiley & Sons, NY (1986)
21. Yorsh, G., Musuvathi, M.: A combination method for generating interpolants. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 353-368. Springer, Heidelberg (2005)