Abstraction-based satisfiability solving of Presburger arithmetic

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

Volumn 3114, Issue , 2004, Pages 308-320

  Kroening, Daniel ^a   Ouaknine, Joël ^a   Seshia, Sanjit A ^a   Strichman, Ofer ^b  

^a Carnegie Mellon University   (United States)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ABSTRACTING; APPROXIMATION ALGORITHMS; COMPUTER AIDED ANALYSIS; DECISION THEORY; DIGITAL ARITHMETIC; ENCODING (SYMBOLS); FORMAL LOGIC; MODEL CHECKING;

DOMAIN SIZE; FINITE DOMAINS; PRESBURGER ARITHMETIC; SAT SOLVERS; SATISFIABILITY; SATISFIABILITY SOLVING; THEOREM PROVERS; UNSATISFIABLE CORE;

THEOREM PROVING;

EID: 35048844329     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-27813-9_24     Document Type: Article

References (33)

1. W. Ackermann. Solvable Cases of the Decision Problem. North-Holland, 1954.
2. T. Amon, G. Borriello, T. Hu, and J. Liu. Symbolic timing verification of timing diagrams using Presburger formulas. In Proceedings of DAC 97, pages 226-231, 1997.
3. G. Audemard, P. Bertoli, A. Cimatti, A. Kornilowicz, and R. Sebastiani. A SAT based approach for solving formulas over boolean and linear mathematical propositions. In Proceedings of CADE 02, pages 195-210, 2002.
4. C. Barrett, D. Dill, and A. Stump. Checking satisfiability of first-order formulas by incremental translation to SAT. In Proceedings of CAV 02, volume 2404, pages 236-249. Springer LNCS, 2002.
5. P. Barth. Logic-Based 0-1 Constraint Programming. Kluwer, 1995.
6. S. Berezin, V. Ganesh, and D. L. Dill. An online proof-producing decision procedure for mixed-integer linear arithmetic. In Proceedings of TACAS 03, volume 2619, pages 521-536. Springer LNCS, 2003.
7. I. Borosh and L. B. Treybig. Bounds on positive integral solutions of linear diophantine equations. Proceedings of the American Mathematical Society, 55(2):299-304, 1976.
8. R. Brinkmann and R. Drechsler. RTL-datapath verification using integer linear programming. In Proceedings of VLSI Design, pages 741-746, 2002.
9. T. Bultan, R. Gerber, and W. Pugh. Symbolic model checking of infinite state systems using Presburger arithmetic. In Proceedings of CAV 97, volume 1254, pages 400-411. Springer LNCS, 1997.
10. P. Chauhan, E. M. Clarke, J. H. Kukula, S. Sapra, H. Veith, and D. Wang. Automated abstraction refinement for model checking large state spaces using SAT based conflict analysis. In FMCAD 02, pages 33-51, 2002.
11. CVC. http://verify.stanford.edu/CVC/.
12. L. de Moura, H. Rueß, and M. Sorea. Lazy theorem proving for bounded model checking over infinite domains. In Proceedings of CADE 02, pages 438-455, 2002.
13. C. Flanagan, R. Joshi, X. Ou, and J. B. Saxe. Theorem proving using lazy proof explication. In Proceedings of CAV 03, volume 2725, pages 355-367, 2003.
14. V. Ganesh, S. Berezin, and D. L. Dill. Deciding Presburger arithmetic by model checking and comparisons with other methods. In Proceedings of FMCAD 02, volume 2517, pages 171-186. Springer LNCS, 2002.
15. T. A. Henzinger, R. Jhala, R. Majumdar, and G. Sutre. Lazy abstraction. In Proceedings of POPL 02, pages 58-70. ACM, 2002.
16. ICS. http://www.icansolve.com.
17. ILOG CPLEX. http://www.ilog.com/products/cplex/.
18. P. Janičič, I. Green, and A. Bundy. A comparison of decision procedures in Presburger arithmetic. Research paper no. 872, Division of Informatics, 1997. University of Edinburgh.
19. R. Kannan and C. L. Monma. On the computational complexity of integer programming problems. In Optimisation and Operations Research, volume 157 of Lecture Notes in Economics and Mathematical Systems, pages 161-172. Springer-Verlag, 1978.
20. R. Kurshan. Computer-Aided Verification of Coordinating Processes. Princeton University Press, 1994.
21. LP_SOLVE. http://www.freshports.org/math/lp_solve/.
22. Math-SAT. http://dit.unitn.it/∼rseba/Mathsat.html.
23. K. McMillan and N. Amla. Automatic abstraction without counterexamples. In Proceedings of TACAS 03, volume 2619, pages 2-17. Springer LNCS, 2003.
24. Moscow ML. http://www.dina.dk/∼sestoft/mosml.html.
25. C. H. Papadimitriou. On the complexity of integer programming. Journal of the ACM, 28(4):765-768, 1981.
26. D. A. Plaisted and S. Greenbaum. A structure-preserving clause form translation. Journal of Symbolic Computation, 2(3):293-304, 1986.
27. M. Preßburger. Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt. Comptesrendus du premier congrès des mathématiciens des pays slaves, 395:92-101, 1929.
28. W. Pugh. The Omega Test: A fast and practical integer programming algorithm for dependence analysis. In Supercomputing, pages 4-13, 1991.
29. R. E. Shostak. A practical decision procedure for arithmetic with function symbols. Journal of the ACM, 26(2):351-360, 1979.
30. UCLID. http://www.cs.cmu.edu/∼uclid.
31. P. Wolper and B. Boigelot. An automata-theoretic approach to Presburger arithmetic constraints. In Proceedings of SAS 95, volume 983, pages 21-32. Springer LNCS, 1995.
32. zChaff. http://www.ee.princeton.edu/∼chaff/zchaff.php.
33. L. Zhang and S. Malik. Extracting small unsatisfiable cores from unsatisfiable boolean formulas. In Proceedings of SAT 03, 2003.