Generating all polynomial invariants in simple loops

Journal of Symbolic Computation

Volumn 42, Issue 4, 2007, Pages 443-476

  Rodriguez Carbonell E ^a   Kapur, D ^b  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b University of New Mexico   (United States)

Author keywords

Gr bner basis; Ideal of polynomials; Loop invariant

Indexed keywords

EID: 34047097816     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2007.01.002     Document Type: Article

References (31)

1. Becker T., and Weispfenning V. Gröbner Bases. A Computational Approach to Commutative Algebra (1993), Springer-Verlag
2. Bressoud D.M. Factorization and Primality Testing (1989), Springer-Verlag
3. Cohen E. Programming in the 1990s (1990), Springer-Verlag
4. Colón M. Approximating the algebraic relational semantics of imperative programs. International Symposium on Static Analysis. SAS 2004. Lecture Notes in Computer Science vol. 3148 (2004), Springer-Verlag 296-311
5. Cousot, P., Cousot, R., 1976. Static determination of dynamic properties of programs. In: Robinet, B. (Ed.), Proceedings of the 2nd International Symposium on Programming, April, pp. 106-130
6. Cousot, P., Cousot, R., 1977. 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, pp. 238-252
7. Cox D., Little J., and O'Shea D. Ideals, Varieties and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra (1996), Springer-Verlag
8. Dershowitz, N., Manna, Z., 1978. Inference rules for program annotation. In: Proceedings of the 3rd International Conference on Software Engineering, pp. 158-167
9. Dijkstra E. A Discipline of Programming (1976), Prentice Hall
10. Freire, P., 2002. www.pedrofreire.com/crea2_en.htm?
11. German S., and Wegbreit B. A synthesizer of inductive assertions. IEEE Transactions on Software Engineering 1 1 (1975) 68-75
12. Gulwani S., and Necula G.C. Precise interprocedural analysis using random interpretation. In: Palsberg J., and Abadi M. (Eds). Proceedings of the 32nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (2005), ACM 324-337
13. Hoare T. The verifying compiler: A grand challenge for computing research. Journal of the ACM 50 1 (2003) 63-69
14. Kaldewaij A. Programming. The Derivation of Algorithms (1990), Prentice-Hall
15. Kapur, D., 2003. Automatically generating loop invariants using quantifier elimination. Technical Report TR-CS-2003-58, Department of Computer Science, UNM. Also in the Proc. of 10th International IMACS Conference on Applications of Computer Algebra, ACA 2004, Lamar, TX, July 2004
16. Karr M. Affine relationships among variables of a program. Acta Informatica 6 (1976) 133-151
17. Katz S., and Manna Z. Logical analysis of programs. Communications of the ACM 19 4 (1976) 188-206
18. Knuth D.E. The Art of Computer Programming. Seminumerical Algorithms vol. 2 (1969), Addison-Wesley
19. Müller-Olm M., and Seidl H. A note on Karr's algorithm. 31 Int. Coll. on Automata, Languages and Programming, ICALP. LNCS vol. 3142 (2004), Springer-Verlag 1016-1028
20. Müller-Olm M., and Seidl H. Computing polynomial program invariants. Information Processing Letters (IPL) 91 5 (2004) 233-244
21. Müller-Olm, M., Seidl, H., 2004b. Precise interprocedural analysis through linear algebra. In: ACM SIGPLAN Principles of Programming Languages, POPL 2004, pp. 330-341
22. Petter, M., 2004. Berechnung von polynomiellen invarianten. Master's Thesis, Fakultät für Informatik, Technische Universität München. Available at http://www2.cs.tum.edu/~petter/da
23. Rodríguez-Carbonell E., and Kapur D. An abstract interpretation approach for automatic generation of polynomial invariants. International Symposium on Static Analysis. SAS 2004. Lecture Notes in Computer Science vol. 3148 (2004), Springer-Verlag 280-295
24. Rodríguez-Carbonell E., and Kapur D. Automatic generation of polynomial loop invariants: Algebraic foundations. International Symposium on Symbolic and Algebraic Computation 2004. ISSAC04 (2004), ACM Press 266-273
25. Rodríguez-Carbonell E., and Kapur D. Program verification using automatic generation of invariants. 1st International Colloquium on Theoretical Aspects of Computing. ICTAC'04. Lecture Notes in Computer Science vol. 3407 (2005), Springer-Verlag 325-340
26. Rodriguez-Carbonell E., and Kapur D. Automatic generation of polynomial invariants of bounded degree using abstract interpretation. Science of Computer Programming 64 1 (2007) 54-75
27. Sankaranarayanan, S., Sipma, H.B., Manna, Z., 2004. Non-linear loop invariant generation using Gröbner bases. In: ACM SIGPLAN Principles of Programming Languages, POPL 2004, pp. 318-329
28. Stanley R. Enumerative Combinatorics vol. 1 (1997), Cambridge University Press
29. Suzuki N., and Ishihata K. Implementation of an array bound checker. Proceedings of the 4th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages (1977), ACM Press 132-143
30. Wegbreit B. The synthesis of loop predicates. Communications of the ACM 17 2 (1974) 102-112
31. Wegbreit B. Property extraction in well-founded property sets. IEEE Transactions on Software Engineering 1 3 (1975) 270-285