Constructing invariants for hybrid systems

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

Volumn 2993, Issue , 2004, Pages 539-554

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

^a Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; DIFFERENTIAL EQUATIONS; ECONOMIC AND SOCIAL EFFECTS;

CONSTRAINT SOLVING; CONTINUOUS DIFFERENTIAL EQUATIONS; DISCRETE TRANSITIONS; INVARIANT GENERATIONS; POLYNOMIAL RINGS; TRADE OFF;

HYBRID SYSTEMS;

EID: 24344439558     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-24743-2_36     Document Type: Article

References (20)

1. BAADER, F., AND NIPKOW, T. Term Rewriting and All That. Cambridge University Press, 1998.
2. 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.
3. BOCKMAYR, A., AND WEISPFENNING, V. Solving numerical constraints. In Handbook of Automated Reasoning, A. Robinson and A. Voronkov, Eds., vol. I. Elsevier Science, 2001, ch. 12, pp. 751-842.
4. COLLINS, G. E., AND HONG, H. Partial cylindrical algebraic decomposition for quantifier elimination. Journal of Symbolic Computation 12, 3 (sep 1991), 299-328.
5. COLÓN, 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.
6. 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.
7. 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.
8. Cox, D., LITTLE, J., AND O'SHEA, D. Ideals, Varieties and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer, 1991.
9. DOLZMANN, A., AND STURM, T. REDLOG: Computer algebra meets computer logic. ACM SIGSAM Bulletin 31, 2 (June 1997), 2-9.
10. HALBWACHS, N., PROY, Y., AND ROUMANOFF, P. Verification of real-time systems using linear relation analysis. Formal Methods in System Design 11, 2 (1997), 157-185.
11. HENZINGER, T., AND Ho, P.H. Algorithmic analysis of nonlinear hybrid systems. In Computer-Aided Verification, P. Wolper, Ed., LNCS 939. 1995, pp. 225-238.
12. HENZINGER, T. A. The theory of hybrid automata. In Logic In Computer Science (LICS 1996) (1996), IEEE Computer Society Press, pp. 278-292.
13. KARR, M. Affine relationships among variables of a program. Acta Inf. 6 (1976), 133-151.
14. LAFFERRIERE, G., PAPPAS, G., AND YOVINE, S. Symbolic reachability computation for families of linear vector fields. J. Symbolic Computation 32 (2001), 231-253.
15. MANNA, Z., AND PNUELI, A. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, New York, 1995.
16. MISHRA, B., AND YAP, C. Notes on Gröbner bases. Information Sciences 48 (1989), 219-252.
17. SANKARANARAYANAN, S., SIPMA, H., AND MANNA, Z. Non-linear loop invariant generation using Gröbner bases. In ACM Principles of Programming Languages (POPL), to appear (2004).
18. TIWARI, A. Approximate reachability for linear systems. In Hybrid Systems: Computation and Control HSCC (2003), vol. 2623 of LNCS, pp. 514-525.
19. TIWARI, A., RUESS, H., SAÏDI, H., AND SHANKAR, N. A technique for invariant generation. In TACAS 2001 (2001), vol. 2031 of LNCS, pp. 113-127.
20. WINDSTEIGER, W., AND BUCHBERGER, B. Gröbner: A library for computing Gröbner bases based on saclib. Tech. rep., RISC-Linz, 1993.