Craig interpolation in the presence of non-linear constraints

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

Volumn 6919 LNCS, Issue , 2011, Pages 240-255

  Kupferschmid, Stefan ^a   Becker, Bernd ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

BMC; Craig Interpolation; Interval Arithmetic; SAT; SMT

Indexed keywords

BMC; BOOLEAN COMBINATIONS; CLOSE INTEGRATION; CONSTRUCTION RULES; CRAIG INTERPOLANTS; CRAIG INTERPOLATION; DECIDABLE THEORY; INTERVAL ARITHMETIC; INTERVAL CONSTRAINT PROPAGATION; LINEAR INEQUALITIES; NON-LINEAR CONSTRAINTS; PROOF TREE; PROPOSITIONAL LOGIC; SAT; TRANSCENDENTAL FUNCTIONS; UNINTERPRETED FUNCTION SYMBOLS; VERIFICATION OF HYBRID SYSTEMS;

BOOLEAN FUNCTIONS; COMPUTABILITY AND DECIDABILITY; HYBRID SYSTEMS; SURFACE MOUNT TECHNOLOGY; TIME SHARING SYSTEMS;

INTERPOLATION;

EID: 80053335955     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-24310-3_17     Document Type: Conference Paper

References (18)

1. Craig, W.: Linear reasoning: A new form of the Herbrand-Gentzen theorem. Journal of Symbolic Logic (3), 250-268 (1957)
2. 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)
3. McMillan, K.L.: An interpolating theorem prover. Theor. Comput. Sci. (1) (2005)
4. Beyer, D., Henzinger, T.A., Jhala, R., Majumdar, R.: The software Model Checker BLAST: Applications to Software Engineering. International Journal on Software Tools for Technology Transfer (STTT) (5-6), 505-525 (2007)
5. Scholl, C., Disch, S., Pigorsch, F., Kupferschmid, S.: Using an SMT solver and Craig interpolation to detect and remove redundant linear constraints in representations of non-convex polyhedra. In: International Workshop on Satisfiability Modulo Theories, pp. 18-26 (2008)
6. Cimatti, A., Griggio, A., Sebastiani, R.: Efficient Generation of Craig Interpolants in Satisfiability modulo theories. In: CoRR (2009)
7. Fränzle, M., Herde, C., Ratschan, S., Schubert, T., Teige, T.: Efficient Solving of Large Non-linear Arithmetic Constraint Systems with Complex Boolean Structure. JSAT Special Issue on Constraint Programming and SAT, 209-236 (2007)
8. Matiyasevich, Y.V.: Enumerable sets are Diophantine. Soviet Mathematics. Doklady 11(2), 354-358 (1970)
9. Davis, M., Logemann, G., Loveland, D.: A Machine Program for Theorem Proving. In: CACM, pp. 394-397 (1962)
10. Davis, M., Putnam, H.: A Computing Procedure for Quantification Theory. Journal of the ACM (3), 201-215 (1960)
11. Benhamou, F., Granvilliers, L.: Continuous and Interval Constraints. In: Handbook of Constraint Programming. Foundations of Artificial Intelligence, pp. 571-603 (2006)
12. Tseitin, G.S.: On the complexity of derivation in propositional calculus. Studies in Constructive Mathematics and Mathematical Logic, Part 2, 115-125 (1970)
13. Kupferschmid, S., Becker, B., Teige, T., Fränzle, M.: Proof certificates and nonlinear arithmetic constraints. In: IEEE Design and Diagnostics of Electronic Circuits and Systems. IEEE, Los Alamitos (2011)
14. 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)
15. Pudlàk, P.: Lower bounds for resolution and cutting planes proofs and monotone computations. J. of Symbolic Logic, 981-998 (1995)
16. Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theoretical Computer Science 138, 3-34 (1995)
17. May, R.M.: Simple Mathematical Models with very Complicated Dynamics. Nature, 459 (1976)
18. Hènon, M.: A two-dimensional mapping with a strange attractor. In: Communications in Mathematical Physics (1976)