An online proof-producing decision procedure for mixed-integer linear arithmetic

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

Volumn 2619, Issue , 2003, Pages 521-536

  Berezin, Sergey ^a   Ganesh, Vijay ^a   Dill, David L ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTERS;

ARITHMETIC CONSTRAINTS; BIT VECTOR; BOOLEAN SATISFIABILITY; DECISION PROCEDURE; MIXED INTEGER LINEAR; OMEGA TEST; STANFORD;

DECISION THEORY;

EID: 35248899420     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-36577-x_38     Document Type: Article

References (21)

1. C. Barrett, D. Dill, and A. Stump. A Framework for Cooperating Decision Procedures. In David McAllester, editor, 17th International Conference on Computer Aided Deduction, volume 1831 of LNAI, pages 79-97. Springer-Verlag, 2000.
2. C. Barrett, D. Dill, and A. Stump. A Generalization of Shostak's Method for Combining Decision Procedures. In 4th International Workshop on Frontiers of Combining Systems (FroCos), 2002.
3. C. Barrett, D. Dill, and A. Stump. Checking Satisfiability of First-Order Formulas by Incremental Translation to SAT. In 14th International Conference on Computer-Aided Verification, 2002.
4. ∼berez/publications.html, 2002.
5. Dimitris Bertsimas and John N. Tsitsiklis. Introduction to Linear Optimization. Athena Scientific, Belmont, Massachusetts, 1997.
6. George B. Dantzig and B. Curtis Eaves. Fourier-Motzkin elimination and its dual. Journal of Combinatorial Theory (A), 14:288-297, 1973.
7. Martin Davis and Hilary Putnam. A computing procedure for quantification theory. Journal of the ACM, 7(3):201-215, July 1960.
8. GMP library for arbitrary precision arithmetic. URL: http://swox.com/gmp.
9. M. Moskewicz, C. Madigan, Y. Zhaod, L. Zhang, and S. Malik. Chaff: Engineering an Efficient SAT Solver. In 39th Design Automation Conference, 2001.
10. M. Oliver Möller. Solving bit-vector equations - a decision procedure for hardware verification, 1998. Diploma Thesis, available at http://www.informatik.uni-ulm.de/ki/Bitvector/.
11. J. Marques-Silva and K. Sakallah. GRASP: A Search Algorithm for Propositional Satisfiability. IEEE Transactions on Computers, 48(5):506-521, 1999.
12. George C. Necula and Peter Lee. Proof generation in the Touchstone theorem prover. In David McAllester, editor, 17th International Conference on Computer-Aided Deduction, volume 1831 of Lecture Notes in Artificial Intelligence. Springer-Verlag, June 2000. Pittsburgh, Pennsylvania.
13. G. Nelson and D. Oppen. Simplification by cooperating decision procedures. ACM Transactions on Programming Languages and Systems, 1(2):245-57, 1979.
14. William Pugh. The omega test: a fast and practical integer programming algorithm for dependence analysis. In Supercomputing, pages 4-13, 1991.
15. H. Ruess and N. Shankar. Deconstructing Shostak. In 16th IEEE Symposium on Logic in Computer Science, 2001.
16. A. Stump, C. Barrett, and D. Dill. CVC: a Cooperating Validity Checker. In 14th International Conference on Computer-Aided Verification, 2002.
17. A. Stump, C. Barrett, D. Dill, and J. Levitt. A Decision Procedure for an Extensional Theory of Arrays. In 16th IEEE Symposium on Logic in Computer Science, pages 29-37. IEEE Computer Society, 2001.
18. R. Shostak. Deciding combinations of theories. Journal of the Association for Computing Machinery, 31(1):1-12, 1984.
19. J. P. M. Silva and K. A. Sakallah. GRASP - A new search algorithm for satisfiability. In Proceedings of the ACM/IEEE International Conference on Computer-Aided Design, pages 220-227, 11 1996.
20. ∼stump/ for a draft.
21. H. P. Williams. Fourier-Motzkin elimination extension to integer programming problems. Journal of Combinatorial Theory (A), 21:118-123, 1976.