Fixed point iteration for computing the time elapse operator

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

Volumn 3927 LNCS, Issue , 2006, Pages 537-551

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

^a NEC LABORATORIES AMERICA   (United States)

^b Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FIXED POINT ITERATION; LIE DERIVATIVES; TIME ELAPSE OPERATOR;

ACCIDENT PREVENTION; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; FUNCTIONS; ITERATIVE METHODS; LINEAR CONTROL SYSTEMS;

OPTIMAL CONTROL SYSTEMS;

EID: 33745803639     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11730637_40     Document Type: Conference Paper

References (20)

1. th Intl. Conference on Computer Aided Verification (2002), vol. 2404 of Lecture Notes in Computer Science, Springer-Verlag, pp. 365-370.
2. BAGNARA, R., HILL, P. M., RICCI, E., AND ZAFFANELLA, E. Precise widening operators for convex polyhedra. In Static Analysis Symposium (2003), vol. 2694 of Lecture Notes in Computer Science, Springer-Verlag, pp. 337-354.
3. BAGNARA, R., RICCI, E., ZAFFANELLA, E., AND HILL, P. M. Possibly not closed convex polyhedra and the Parma Polyhedra Library. In Static Analysis Symposium (2002), vol. 2477 of Lecture Notes in Computer Science, Springer-Verlag, pp. 213-229.
4. BESSON, F., JENSEN, T., AND TALPIN, J.-P. Polyhedral analysis of synchronous languages. In Static Analysis Symposium (1999), vol. 1694 of Lecture Notes in Computer Science, Springer-Verlag, pp. 51-69.
5. 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.
6. COUSOT, P., AND COUSOT, R. Comparing the Galois connection and widening/narrowing approaches to Abstract interpretation, invited paper. In PLILP '92 (1992), vol. 631 of Lecture Notes in Computer Science, Springer-Verlag, pp. 269-295.
7. DAVEY, B. A., AND PRIESTLY, H. A. Introduction to Lattices and Order. Cambridge University Press, 1990.
8. FEHNKER, A., AND IVANČIĆ, F. Benchmarks for hybrid systems verification. In Hybrid Systems: Computation and Control (HSCC 2004) (2004), vol. 2993 of Lecture Notes in Computer Science, Springer-Verlag, pp. 326-341.
9. FREHSE, G. PHAVer: Algorithmic verification of hybrid systems past HyTech. In Hybrid Systems: Computation and Control (HSCC 2005) (2005), vol. 2289 of Lecture Notes in Computer Science, Springer-Verlag, pp. 258-273.
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., vol. 939 of Lecture Notes in Computer Science. Springer-Verlag, 1995, pp. 225-238.
12. LAFFERRIERE, G., PAPPAS, G., AND YOVINE, S. Symbolic reachability computation for families of linear vector fields. J. Symbolic Computation 32 (2001), 231-253.
13. PIAZZA, C., ANTONIOTTI, M., MYSORE, V., POLICRITI, A., WINKLER, F., AND MISHRA, B. Algorithmic algebraic model checking I: Challenges from systems biology. In Computer-aided Verification (2005), vol. 3576 of Lecture Notes in Computer Science, Springer-Verlag, pp. 5-19.
14. PRAJNA, S., AND JADBABAIE, A. Safety verification using barrier certificates. In Hybrid Systems: Computation and Control (2004), vol. 2993 of Lecture Notes in Computer Science, Springer-Verlag, pp. 477-492.
15. RATSCHAN, S., AND SHE, Z. Safety verification of hybrid systems by constraint propagation based abstraction refinement. In HSCC (2005), vol. 3414 of Lecture Notes in Computer Science, Springer-Verlag, pp. 573-589.
16. RODRIGUEZ-CARBONELL, E., AND TIWARI, A. Generating polynomial invariants for hybrid systems. In Hybrid Systems: Computation and Control, HSCC 2005 (2005), vol. 3414 of LNCS, Springer, pp. 590-605.
17. SANKARANARAYANAN, S., SIPMA, H. B., AND MANNA, Z. Constructing invariants for hybrid systems. In Hybrid Systems: Computation and Control (HSCC 2004) (march 2004), vol. 2993 of Lecture Notes in Computer Science, Springer-Verlag, pp. 539-555.
18. SILVA, B., RICHESON, K., KROGH, B. H., AND CHUTINAN, A. Modeling and verification of hybrid dynamical system using checkmate. In ADPM 2000 (2000). available online from http://www.ece.cmu.edu/~webk/checkmate.
19. TIWARI, A. Approximate reachability for linear systems. In Hybrid Systems: Computation and Control HSCC (2003), vol. 2623 of Lecture Notes in Computer Science, Springer-Verlag, pp. 514-525.
20. TIWARI, A., AND KHANNA, G. Non-linear systems: Approximating reach sets. In Hybrid Systems: Computation and Control (2004), vol. 2993 of Lecture Notes in Computer Science, Springer-Verlag, pp. 477-492.