Algorithmic algebraic model checking II: Decidability of semi-algebraic model checking and its applications to systems biology

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

Volumn 3707 LNCS, Issue , 2005, Pages 217-233

  Mysore, V ^a   Piazza, C ^b   Mishra, B ^a,c  

^a NEW YORK UNIVERSITY   (United States)

^b UNIVERSITY OF UDINE   (Italy)

^c NEW YORK UNIVERSITY SCHOOL OF MEDICINE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BIOCHEMISTRY; CODES (SYMBOLS); COMPUTABILITY AND DECIDABILITY; MATHEMATICAL MODELS;

BIOCHEMICAL NETWORKS; BOUNDED REACHABILITY; SEMI-ALGEBRAIC HYBRID SYSTEMS; TIMED COMPUTATION TREE LOGIC;

ALGEBRA;

EID: 33646196701     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11562948_18     Document Type: Conference Paper

References (33)

1. R. Alur, C. Courcoubetis, and D. Dill. Model-Checking for Real-Time Systems. In International Symposium on Logic in Computer Science, 5, pages 414-425. IEEE Computer Press, 1990.
2. R. Alur, C. Courcoubetis, N. Halbwachs, T. A. Henzinger, P.-H. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine. The Algorithmic Analysis of Hybrid Systems. Theoretical Computer Science, 138:3-34, 1995.
3. R. Alur, T. Dang, and F. Ivancic. Progress on Reachability Analysis of Hybrid Systems Using Predicate Abstraction, In O. Maler and A. Pnueli, editors, Hybrid Systems: Computation and Control (JISCC'03), volume 2623 of LNCS, pages 4-19, Springer-Verlag, 2003.
4. Hirokazu Anai. Algebraic approach to analysis of discrete-time polynomial systems. In ECC Karlsure (Germany), 1999.
5. M. Antoniotti, A. Policriti, N. Ugel, and B. Mishra. Reasoning about Biochemical Processes. Cell Biochemistry and Biophysics, 38:271-286, 2003.
6. E. Asarin, T. Dang, O. Maler, and O. Bournez. Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems. In B. Krogh and N. Lynch, editors, Hybrid Systems: Computation and Control (HSCC'00), volume 1790 of LNCS, pages 20-31. Springer-Verlag, 2000.
7. L. Blum, F. Cucker, M. Shub, and S. Smale. Complexity and Real Computation, Springer-Verlag, 1997.
8. O. Bournez, O. Maler, and A. Pnueli. Orthogonal Polyhedra: Representation and Computation. In P. Vaadrager and J. van Schuppen, editors, Hybrid Systems: Computation and Control (HSCC 1999), volume 1596 of LNCS, pages 19-30. SpringerVerlag, 1999.
9. A. Chutinan and B. Krogh. Verification of Polyhedral-Invariant Hybrid Automata Using Polygonal Plow Pipe Approximations. In F. W. Vaandrager and J. H. van Schuppen, editors, Hybrid Systems: Computation and Control (HSCC'99), volume 1569 of LNCS, pages 76-90. Springer-Verlag, 1999.
10. J. R. Collier, N. A. M. Monk, P. K. Maini, and J. H. Lewis. Pattern Formation by Lateral Inhibition with Feedback: a Mathematical Model of Delta-Notch Intercellular Signalling. Journal of Theor. Biology, 183:429-446, 1996.
11. G. E. Collins. Quantifier Elimination for the Elementary Theory of Real Closed Fields by Cylindrical Algebraic Decomposition. In Proceedings of the Second GI Conference on Automata Theory and Formal Languages, volume 33 of LNCS, pages 134-183. Springer-Verlag, 1975.
12. Andreas Dolzmann and Thomas Sturm. REDLOG: Computer algebra meets computer logic. SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation), 31(2):2-9, 1997.
13. Martin Fränzle. What will be eventually true of polynomial hybrid automata? In Naoki Kobayashi and Benjamin C. Pierce, editors, Theoretical Aspects of Computer Software, 4th International Symposium, TACS 2001, Sendai, Japan, October 29-31, 2001, Proceedings, volume 2215 of Lecture Notes in Computer Science, pages 340-359. Springer, 2001.
14. R. Ghosh and C. Tomlin. Lateral Inhibition through Delta-Notch signaling: A Piecewise Affine Hybrid Model. In M. D. D. Benedetto and A. Sangiovanni-Vincentelli, editors, Int.l Workshop on Hybrid Systems: Computation and Control (HSCC'01), volume 2034 of LNCS, pages 232-246. Springer-Verlag, 2001.
15. Esfandiar Haghverdi, Paulo Tabuada, and George J. Pappas. Bisimulation relations for dynamical, control, and hybrid systems. Theoretical Computer Science, November 2003.
16. T. Henzinger, P. W. Kopke, A. Puri, and P. Varaiya. What's Decidable about Hybrid Automata. In Symposium on the Theory of Computing (STOC), pages 373-382, 1995.
17. T. A. Henzinger, X. Nicollin, J. Sifakis, and S. Yovine. Symbolic Model Checking for Real-time Systems. In 7th Annual IEEE Symposium on Logic in Computer Science, pages 394-406. IEEE, IEEE Computer Society Press, June 1992.
18. H. Hong. Quantifier elimination in elementary algebra and geometry by partial cylindrical algebraic decomposition, version 13. WWW site www.eecis.udel.edu/~saclib, 1995.
19. Inseok Hwang, Hamsa Balakrishnan, Ronojoy Ghosh, and Claire Tomlin. Reachability analysis of delta-notch lateral inhibition using predicate abstraction. Lecture Notes in Computer Science, 2552:715-724, Jan 2002.
20. Mats Jirstrand. Nonlinear control system design by quantifier elimination. J. Symb. Comput., 24(2):137-152, 1997.
21. G. Lafferiere, G. J. Pappas, and S. Sastry. O-minimal Hybrid Systems. Mathematics of Control, Signals, and Systems, 13(1):1-21, March 2000.
22. Gerardo Lafferriere, George J. Pappas, and Sergio Yovine. Symbolic reachability computation for families of linear vector fields. J. Symb. Comput., 32(3):231-253, 2001.
23. R. Lanotte and S.Tini. Taylor approximation for hybrid systems. In HSCC. LNCS, 2005.
24. B. Mandelbrot. The Fractal Geometry of Nature. Freeman Co., San Francisco, 1982.
25. B. Mishra. A Symbolic Approach to Modeling Cellular Behavior. In S. Sahni, V. K. Prasanna, and U. Shukla, editors, High Performance Computing (HiPC'02), volume 2552 of LNCS, pages 725-732. Springer-Verlag, 2002.
26. B. Mishra. Computational Real Algebraic Geometry. CRC Press, Boca Raton, PL, 2004.
27. V. Mysore and B. Mishra. Algorithmic Algebraic Model Checking III: Approximate Methods. In Third International Symposium on Automated Technology for Verification and Analysis (ATVA), 2005.
28. C. Piazza, M. Antoniotti, V. Mysore, A. Policriti, F. Winkler, and B. Mishra. Algorithmic Algebraic Model Checking I: The Case of Biochemical Systems and their Reachability Analysis. In 17th International Conference on Computer Aided Verification (CAV), 2005.
29. A. Puri and P. Varaiya. Decidebility of hybrid systems with rectangular differential inclusions. Computer Aided Verification, pages 95-104, 1994.
30. C. Robinson. Dynamical Systems: Stability, Symbolic Dynamics, and Chaos. CRC Press, Boca Raton, 1995.
31. Paulo Tabuada and George J. Pappas. Model checking Itl over controllable linear systems is decidable. Hybrid Systems: Computation and Control, Lecture Notes in Computer Science, 2623, April 2003.
32. A. Tarski. A Decision Method for Elementary Algebra and Geometry. University of California Press, second edition, 1948.
33. A. Tiwari and G. Khanna. Series of Abstraction for Hybrid Automata. In C. J. Tomlin and M. Greenstreet, editors, Hybrid Systems: Computation and Control (HSCC'02), volume 2289 of LNCS, pages 465-478. Springer-Verlag, 2002.