A quantifier-elimination based heuristic for automatically generating inductive assertions for programs

Journal of Systems Science and Complexity

Volumn 19, Issue 3, 2006, Pages 307-330

  Kapur, Deepak ^a  

^a University of New Mexico   (United States)

Author keywords

Automated software analysis and verification; Inductive assertion; Loop invariant; Quantifier elimination

Indexed keywords

EID: 33749262808     PISSN: 10096124     EISSN: 15597067     Source Type: Journal    
DOI: 10.1007/s11424-006-0307-x     Document Type: Article

References (34)

1. B. Elspas, M. W. Green, K. N. Levitt, and R. J. Waldinger, Research in Interactive Program-Proving Techniques, Stanford Research Institute, Menlo Park, California, USA, May 1972.
2. S. German and B. Wegbreit, A synthesizer of inductive assertions, IEEE Transactions on Software Engineering, 1975, 1(1): 68-75.
3. S. Katz and Z. Manna, Logical analysis of programs, Communications of the ACM, 1976, 19(4): 188-206.
4. P. Cousot and R. Cousot, Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints, in Conference Record of the Fourth Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, Los Angeles, California, ACM Press, New York, NY, 1977, 238-252.
5. P. Cousot and N. Halbwachs, Automatic discovery of linear restraints among variables of a program, in Conference Record of the Fifth Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, Tucson, Arizona, ACM Press, New York, NY, 1978, 84-97.
6. M. Müller-Olm and H. Seidl, Polynomial constants are decidable, in 9th Static Analysis Symposium (SAS) (LNCS 2477), Springer-Verlag, 2002.
7. M. Müller-Olm and H. Seidl, Precise interprocedural analysis through linear algebra, in Symposium on Principles of Programming Languages, 2004, 330-341.
8. E. Rodríguez-Carbonell and D. Kapur, An abstract interpretation approach for automatic generation of polynomial invariants, in 11th Symposium on Static Analysis (SAS) (LNCS 3148), Verona, Italy, Springer-Verlag, August 2004, 280-295.
9. W. Wu, On the decision problem and the mechanization of theorem proving in elementary geometry, Scientia Sinica, 1978, 21: 150-172.
10. W. Wu, Basic principles of mechanical theorem proving in geometries, J. of Automated Reasoning, 1986, 2: 221-252.
11. S. C. Chou, Mechanical Geometry Theorem Proving, D. Reidel Publishing Company, Dordrecht, Netherlands, 1988.
12. D. Kapur, Geometry theorem proving using Hilbert's Nullstellensatz, in Proc. 1986 Symposium on Symbolic and Algebraic Computation (SYMSAC 86), 1986, 202-208.
13. D. Kapur, A refutational approach to Geometry theorem proving, Artificial Intelligence, 1988, 37: 61-93.
14. B. Wegbreit, The synthesis of loop predicates, Communications of the ACM, 1974, 17(2): 102-112.
15. B. Wegbreit, Property extraction in well-founded property sets, IEEE Transactions on Software Engineering, 1975, 1(3): 270-285.
16. M. Karr, Affine relationships among variables of a program, Acta Information, 1976, 6: 133-151.
17. M. A. Colon, S. Sankaranarayanan, and H. B. Sipma, Linear invariant generation using non-linear constraint solving, in Computer-Aided Verification (CAV 2003), Lecture Notes in Computer Science, Springer Verlag, 2003, 2725: 420-432.
18. E. Rodríguez-Carbonell and D. Kapur, Automatic generation of polynomial loop invariants: Algebraic foundations, in Intl. Symp. on Symbolic and Algebraic Computation (ISSAC), Santander, Spain, July 2004, 266-273.
19. E. Rodríguez-Carbonell and D. Kapur, Automatic generation of polynomial loop invariants for imperative programs, in Intl. Colloquium on Theoretical Aspects of Computing (ICTAC 2004) (LNCS 3407), China, Springer-Verlag, Feb. 2005, 325-340.
20. S. Sankaranarayanan, H. B. Sipma, and Z. Manna, Non-linear loop invariant generation using Gröbner Bases, in Symp. on Principles of Programming Languages, 2004, 318-329.
21. D. Kapur, An approach for solving systems of parametric polynomial equations, in Principles and Practices of Constraint Programming (ed. by Saraswat and Van Hentenryck), MIT Press, 1995, 217-244.
22. V. Weispfenning, A Comprehensive Gröbner Basis Algorithm, J. of Symbolic Computation, July 1992, 14: 1-29.
23. H. Enderton, Mathematical Logic, An Introduction, Academic Press, 1992.
24. D. Kapur and X. Nie, Reasoning about numbers in Tecton, in Proceedings 8th International Symposium on Methodologies for Intelligent Systems (ISMIS'94), October 1994, 57-70.
25. D. Kapur and H. Zhang, An overview of rewrite rule laboratory (RRL), Journal of Computer and Mathematics with Applications, 1995, 29: 91-114.
26. R. Loos and V. Weispfenning, Applying linear quantifier elimination, Computer Journal, 1993, 36(5): 450-462.
27. A. Lasaruk and T. Sturm, Weak quantifier elimination for the full linear theory of the integers - A uniform generalization of Presburger arithmetic, Technical Report, MIP-0604, University of Passau, April 2006.
28. A. Schrijver, Theory of Linear and Integer Programming, John Wiley, 1998.
29. V. Weispfenning, Complexity and uniformity of elimination in Presburger arithmetic, in Intl. Symp. on Symbolic and Algebraic Computation (ISSAC), Maui, US, July 1997, 48-53.
30. V. Weispfenning, The complexity of almost linear Diophantine problems, Journal of Symbolic Computation, 1990, 10: 395-403.
31. G. Collins and H. Hong, Partial cylindrical algebraic decomposition for quantifier elimination, Journal of Symbolic Computation, 1991, 12(3): 299-328.
32. A. Doltzmann and T. Sturm, REDLOG: Computer algebra meets computer logic, MIP-9603, Technical Report, University of Passau, Sep. 1996.
33. H. Hong, et al., http://www.cs.usna.edu/qepcad/B/WhatisQEPCAD.html.
34. A. Doltzmann, T. Sturm, and V. Weispfenning, Real quantifier elimination in practice, Technical Report, MIP-9720, University of Passau, Dec. 1997.