Deciding presburger arithmetic by model checking and comparisons with other methods

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

Volumn 2517, Issue , 2002, Pages 171-186

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

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATA THEORY; BINARY DECISION DIAGRAMS; BOOLEAN FUNCTIONS; COMPUTER AIDED DESIGN; DIGITAL ARITHMETIC; FORMAL METHODS;

MODEL CHECKER; MODEL CHECKING PROBLEM; NUMBER OF STATE; PARAMETERIZED; PRESBURGER; PRESBURGER ARITHMETIC; SATISFIABILITY PROBLEMS; TEST CASE;

MODEL CHECKING;

EID: 23044532366     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-36126-x_11     Document Type: Conference Paper

References (19)

1. Tod Amon, Gaetano Borriello, Taokuan Hu, and Jiwen Liu. Symbolic timing verification of timing diagrams using Presburger formulas. In Design Automation Conference, pages 226–231, 1997.
2. Alexandre Boudet and Hubert Comon. Diophantine equations, Presburger arithmetic and finite automata. In H. Kirchner, editor, Colloquium on Trees in Algebra and Programming (CAAP’96), volume 1059 of Lecture Notes in Computer Science, pages 30–43. Springer Verlag, 1996.
3. R. Brinkmann and R. Drechsler. RTL-datapath verification using integer linear programming. In IEEEVLSI Design’01andAsia and South Pacific DesignAutomation Conference, Bangalore, pages 741–746, 2002.
4. R. E. Bryant. Graph-based algorithms for boolean function manipulation. IEEE Transactions on Computers, 35(8):677–691, 1986.
5. J. R. Büchi. Weak second-order arithmetic and finite automata. Zeitschrift für mathematische Logik und Grundladen der Mathematik, 6:66–92, 1960.
6. J. R. Burch, E. M. Clarke, K. L. McMillan, D. L. Dill, and L. J. Hwang. Symbolic model checking: 1020 states and beyond. Information and Computation, 98:142–170, 1992.
7. E. M. Clarke, E. A. Emerson, and A. P. Sistla. Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Transactions on Programming Languages and Systems, 8(2):244–263, 1986.
8. D. C. Cooper. Theorem proving in arithmetic without multiplication. In Machine Intelligence, volume 7, pages 91–99, New York, 1972. American Elsevier.
9. George B. Dantzig and B. Curtis Eaves. Fourier-Motzkin elimination and its dual. Journal of Combinatorial Theory (A), 14:288–297, 1973.
10. Jacob Elgaard, Nils Klarlund, and Anders Møller. Mona 1.X: New techniques for ws1s and ws2s. In Computer AidedVerification, CAV ’98, Proceedings, volume 1427 of LNCS. Springer Verlag, 1998.
11. P. Johannsen and R. Drechsler. Formal verification on the RT level computing one-to-one design abstractions by signal width reduction. In IFIP International Conference on Very Large Scale Integration (VLSI’01), Montpellier, 2001, pages 127–132, 2001.
12. G. Kreisel and J. Krivine. Elements of mathematical logic, 1967.
13. K. L. McMillan. Symbolic Model Checking: An Approach to the State Explosion Problem. Kluwer Academic Publishers, 1993.
14. Derek C. Oppen. A 222pn upper bound on the complexity of Presburger arithmetic. Journal of Computer and System Sciences, 16(3):323–332, June 1978.
15. M. Presburger. Uber de vollstandigkeit eines gewissen systems der arithmetik ganzer zahlen, in welchen, die addition als einzige operation hervortritt. In Comptes Rendus du Premier Congres des Mathematicienes des Pays Slaves, pages 92–101, 395,Warsaw, 1927.
16. William Pugh. The omega test: A fast and practical integer programming algorithm for dependence analysis. In Supercomputing, pages 4–13, 1991.
17. T. R. Shiple, J. H. Kukula, and R. K. Ranjan. A comparison of Presburger engines for EFSM reachability. In A. J. Hu and M. Y. Vardi, editors, Proceedings of the 10th International Conference on Computer Aided Verification, volume 1427, pages 280–292. Springer-Verlag, 1998.
18. H. P. Williams. Fourier-Motzkin elimination extension to integer programming problems. Journal of Combinatorial Theory (A), 21:118–123, 1976.
19. Pierre Wolper and Bernard Boigelot. On the construction of automata from linear arithmetic constraints. In Proc. 6th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, volume 1785 Of Lecture Notes in Computer Science, pages 1–19, Berlin, March 2000. Springer-Verlag.