Non-linear loop invariant generation using gröbner bases

Conference Record of the Annual ACM Symposium on Principles of Programming Languages

Volumn 31, Issue , 2004, Pages 318-329

  Sankaranarayanan, Sriram ^a   Sipma, Henny B ^a   Manna, Zohar ^a  

^a Stanford University   (United States)

Author keywords

Constraint Programming; Gr bner Bases; Ideals; Invariant Generation; Program Analysis; Symbolic Computation; Verification

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; CONSTRAINT THEORY; HEURISTIC METHODS; ITERATIVE METHODS; LINEAR PROGRAMMING; POLYNOMIALS; PROBLEM SOLVING;

CONSTRAINT PROGRAMMING; GRÖBNER BASES; IDEALS; INVARIANT GENERATION; PROGRAM ANALYSIS; SYMBOLIC COMPUTATION; VERIFICATION;

COMPUTER PROGRAMMING LANGUAGES;

EID: 2442424185     PISSN: 07308566     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/964001.964028     Document Type: Conference Paper

References (30)

1. BAADER, F., AND NIPKOW, T. Term Rewriting and All That. Cambridge University Press, 1998.
2. BALLARIN, C., AND KAUERS, M. Solving parametric linear systems: an experiment with constraint algebraic programming. In Eighth Rhine Workshop on Computer Algebra (2002), pp. 101-114.
3. BENSALEM, S., BOZGA, M., FERNANDEZ, J.-C., GHIRVU, L., AND LAKHNECH, Y. A transformational approach for generating non-linear invariants. In Static Analysis Symposium (June 2000), vol. 1824 of LNCS, Springer Verlag.
4. BENSALEM, S., LAKHNECH, Y., AND SAIDI, H. Powerful techniques for the automatic generation of invariants. In Computer-Aided Verification (1996), vol. 1102 of LNCS, pp. 323-335.
5. BJØRNER, N. S., BROWNE, A., AND MANNA, Z. Automatic generation of invariants and intermediate assertions. Theoretical Comput. Sci. 173, 1 (Feb. 1997), 49-87.
6. BULTAN, T., GERBER, R., AND PUGH, W. Symbolic model checking of infinite state systems using Presburger arithmetic. In Computer-Aided Verification (June 1997), vol. 1254 of LNCS, springer, pp. 400-411.
7. COLLINS, G. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In Automata Theory and Formal Languages (1975), H.Brakhage, Ed., vol. 33 of LNCS, pp. 134-183.
8. COLLINS, G. E., AND HONG, H. Partial cylindrical algebraic decomposition for quantifier elimination. Journal of Symbolic Computation 12, 3 (sep 1991), 299-328.
9. COLON, M., SANKARANARAYANAN, S., AND SIPMA, H. Linear invariant generation using non-linear constraint solving. In Computer Aided Verification (July 2003), F. Somenzi and W. H. Jr, Eds., vol. 2725 of LNCS, Springer Verlag, pp. 420-433.
10. COUSOT, P., AND COUSOT, R. Abstract Interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In ACM Principles of Programming Languages (1977), pp. 238-252.
11. COUSOT, P., AND HALBWACHS, N. Automatic discovery of linear restraints among the variables of a program. In ACM Principles of Programming Languages (Jan. 1978), pp. 84-97.
12. COX, D., LITTLE, J. AND O'SHEA, D. Ideals, Varieties and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer, 1991.
13. DOLZMANN, A., AND STURM, T. REDLOG: Computer algebra meets computer logic. ACM SIGSAM Bulletin 31, 2 (June 1997), 2-9.
14. FLOYD, R. W. Assigning meanings to programs. Proc. Symposia in Applied Mathematics 19 (1967), 19-32.
15. HENZINGER, T. A., AND Ho, P. HYTECH: The Cornell hybrid technology tool. In Hybrid Systems II (1995), vol. 999 of LNCS, pp. 265-293.
16. HOARE, C. A. R. An axiomatic basis for computer programming. Commun. ACM 12, 10 (1969), 576-580.
17. JAFFAR, J., AND LASSEZ, J.-L. Constraint logic programming. In Principles of Programming Languages(POPL) (Jan. 1987), pp. 111-119.
18. KARR, M. Affine relationships among variables of a program. Acta Inf. 6 (1976), 133-151.
19. MANNA, Z. Mathematical Theory of Computation. McGraw-Hill, 1974.
20. MANNA, Z., AND PNUELI, A. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, New York, 1995.
21. MISHRA, B., AND YAP, C. Notes on Gröbner bases. Information Sciences 48 (1989), 219-252.
22. MÜLLER-OLM, M., AND SEIDL, H. Polynomial constants are decidable. In Static Analysis Symposium (SAS 2002) (2002), vol. 2477 of LNCS, pp. 4-19.
23. SCHRIJVER, A. Theory of Linear and Integer Programming. Wiley, 1986.
24. SIT, W. Y. An algorithm for solving parametric linear systems. Journal of Symbolic Computation 13, 3 (April 1992), 353-394.
25. TARSKI, A. A decision method for elementary algebra and geometry. Univ. of California Press, Berkeley 5 (1951).
26. TIWARI, A., RUESS, H., SAÏDI, H., AND SHANKAR, N. A technique for invariant generation. In TACAS 2001 (2001), vol. 2031 of LNCS, Springer-Verlag, pp. 113-127.
27. WEISPFENNING, V. The complexity of linear problems in fields. Journal of Symbolic Computation 5, 1-2 (April 1988), 3-27.
28. WEISPFENNING, V. Comprehensive Gröbner bases. Journal of Symbolic Computation 14 (1992), 1-29.
29. WEISPFENNING, V. Quantifier elimination for real algebra-the quadratic case and beyond. In Applied Algebra and Error-Correcting Codes (AAECC) 8 (1997), pp. 85-101.
30. WINDSTEIGER, W., AND BUCHBERGER, B. Groebner: A library for computing grob̈ner bases based on saclib. Tech. rep., RISC-Linz, 1993.