On hybrid systems and the modal□-calculus

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

Volumn 1567, Issue , 1999, Pages 38-69

  Davoren, J M ^a  

^a Cornell University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ABSTRACTING; AUTOMATA THEORY; CALCULATIONS; COMPUTER CIRCUITS; CONTINUOUS TIME SYSTEMS; EQUIVALENCE CLASSES; FORMAL LOGIC; HYBRID SYSTEMS; INTERACTIVE COMPUTER SYSTEMS; MODAL ANALYSIS; REAL TIME SYSTEMS; SET THEORY; SYSTEM THEORY;

CONTINUITY PROPERTIES; DEDUCTIVE VERIFICATION; DISCRETE ABSTRACTION; DISCRETE TRANSITIONS; FINITE STATE SPACES; SET-VALUED FUNCTIONS; SYMBOLIC REPRESENTATION; TRANSITION RELATIONS;

DISCRETE TIME CONTROL SYSTEMS;

EID: 84956858069     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-49163-5_3     Document Type: Conference Paper

References (40)

1. E. Akin, The General Topology of Dynamical Systems, Graduate Studies in Mathematics 1 (American Mathematical Society, Providence, 1993).
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 (1995) 3-34.
3. R. Alur and D. L. Dill, “A Theory of Timed Automata", Theoretical Computer Science 126 (1994) 183-235.
4. R. Alur, T. A. Henzinger and P.-H. Ho, “Automatic Symbolic Verification of Embedded Systems", IEEE Transactions on Software Engineering 22 (1996) 181-201.
5. S. Ambler, M. Kwiatkowska and N. Measor, “Duality and the Completeness of the Modal-calculus", Theoretical Computer Science 151 (1995) 3-27.
6. J-P. Aubin and H. Frankasowa, Set-Valued Analysis (Birkhäuser, Boston, 1990).
7. J-P. Aubin, Viability Theory (Birkhäuser, Boston, 1991).
8. M. M. Bonsangue and M. Z. Kwiatkowska, “Reinterpreting the Modal-calculus", in A. Ponse, M. de Rijke and Y. Venema (eds.), Modal Logic and Process Algebra, CSLI Lecture Notes 53 (CLSI Publications, Stanford, 1995); 65-83.
9. B. F. Chellas, Modal Logic: An Introduction (Cambridge University Press, 1980).
10. J. M. Davoren, Modal Logics for Continuous Dynamics, PhD dissertation, Department of Mathematics, Cornell University, January 1998.
11. J. M. Davoren, “Topologies, Continuity and Bisimulations", presented at Fixed Points in Computer Science, Brno, August 1998; submitted for publication.
12. J. M. Davoren, “On Continuous Dynamics and Modal Logics", in preparation.
13. C. Daws, A. Olivero, S. Tripakis and S. Yovine, “The Tool Kronos", in R. Alur, T. A. Henzinger and E. D. Sontag (eds.), Hybrid Systems III, Lecture Notes in Computer Science 1066 (Springer-Verlag, Berlin, 1996); 208-219.
14. L. van den Dries, Tame Topology and O-minimal Structures, London Mathematical Society Lecture Notes Series 248 (Cambridge University Press, 1998).
15. E. A. Emerson, “Modal Checking and the Mu-calculus", in N. Immerman and P. G. Kolaitis (eds.), Descriptive Complexity and Finite Models, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 31 (American Mathematical Society, Providence, 1997); 185-208.
16. R. Fagin, J. Y. Halpern, Y. Moses and M. Y. Vardi, Reasoning About Knowledge (MIT Press, Cambridge MA, 1995).
17. V. Gupta, T. A. Henzinger and R. Jagadeesan, “Robust Timed Automata", in O. Maler (ed.), Hybrid and Real-Time Systems: International Workshop HART'97, March 1997, Lecture Notes in Computer Science 1201 (Springer-Verlag, Berlin, 1997); 331-345.
18. L. Henkin, “Completeness in the Theory of Types", Journal of Symbolic Logic 15 (1950) 81-91.
19. th An-nual IEEE Symposium on Logic in Computer Science (LICS '96) (IEEE Computer Society Press, 1996); 278-292.
20. T. A. Henzinger, O. Kupferman, and S. Qadeer, “From Pre-historic to Post-modern Symbolic Model Checking", Proceedings of the Tenth International Conference on Computer-aided Verification (CAV 1998), Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1998).
21. T. A. Henzinger, Z. Manna and A. Pnueli, “Towards Refining Temporal Specifications into Hybrid Systems", in R. Grossman et al. (eds.), Hybrid Systems, Lecture Notes in Computer Science 736 (Springer-Verlag, Berlin, 1993), 60-76.
22. M. J. Hollenberg, Logic and Bisimulation, PhD dissertation, Department of Philosophy, Utrecht University, March 1998.
23. D. Kozen, “Results on the Propositional-Calculus", Theoretical Computer Sci-ence 27 (1983) 333-354.
24. K. Kuratowski, Topology, Volume 1, revised edition (Academic Press, New York, 1966). Translated by J. Jaworowski from the French 1958 edition of Topologie, Volume 1, Polska Akademia Nauk Monograé Matematyczne, Tom 21 (Pafinstwowe Wydawnictwo Naukowe, Warsaw, 1958).
25. D. Janin and I. Walukiewicz, “On the expressive completeness of the propositional mu-calculus with respect to monadic second order logic", Proceedings of the Seventh International Conference on Concurrency Theory (CONCUR'96), Lecture Notes in Computer Science 1119 (Springer-Verlag, Berlin, 1996), 263-277.
26. B. Jónsson and A. Tarski, “Boolean Algebras with Operators, Part I", American Journal of Mathematics 73 (1951) 891-939.
27. G. Laérriere, G. J. Pappas and S. Sastry, “O-Minimal Hybrid Systems", Technical report UCB/ERL M98/29, Department of Electrical Engineering and Computer Science, University of California at Berkeley, May 1998.
28. G. Laérriere, G. J. Pappas and S. Yovine, “Decidable Hybrid Systems", Technical report UCB/ERL M98/39, Department of Electrical Engineering and Computer Science, University of California at Berkeley, June 1998.
29. Z. Manna and A. Pnueli, “Verifying Hybrid Systems", in R. Grossman et al. (eds.), Hybrid Systems, Lecture Notes in Computer Science 736 (Springer-Verlag, Berlin, 1993), 4-35.
30. Z. Manna and H. B. Simpa, “Deductive Verification of Hybrid Systems Using STeP", in T. A. Henzinger and S. Sastry (eds), Hybrid Systems-Computation and Control: Proceedings of the First International Workshop (HSCC '98), Lecture Notes in Computer Science 1386, (Springer-Verlag, Berlin, 1998).
31. J. C. C. McKinsey, “A Solution of the Decision Problem for the Lewis Systems S2 and S4, with an Application to Topology", Journal of Symbolic Logic 6 (1941) 117-134.
32. J. C. C. McKinsey and A. Tarski, “The Algebra of Topology", Annals of Mathe-matics 45 (1944) 141-191.
33. J. R. Munkres, Topology: A First Course (Prentice Hall, Englewood Cliffis, 1975).
34. A. Nerode and W. Kohn, “Models for Hybrid Systems: Automata, Topologies, Controllability, Observability", in R. Grossman et al. (eds.), Hybrid Systems, Lecture Notes in Computer Science 736 (Springer-Verlag, Berlin, 1993), 297-316.
35. A. Nerode and R. Shore, Logic for Applications (2nd ed.), Graduate Texts in Computer Science (Springer-Verlag, Berlin, 1997).
36. H. Rasiowa and R. Sikorski, The Mathematics of Metamathematics, Polska Akademia Nauk Monograé Matematyczne, Tom 41 (Pafinstwowe Wydawnictwo Naukowe, Warsaw, 1963).
37. M. B. Smyth, “Semi-metrics, closure spaces and digital topology", Theoretical Computer Science 151 (1995) 257-276.
38. C. Stirling, “Modal and Temporal Logics", in S. Abramsky, D. M. Gabbay and T. Maibaum (eds.), Handbook of Logic in Computer Science, Vol. 2: Computational Structures (Oxford University Press, Clarendon Press, Oxford, 1992), 477-563
39. I. Walukiewicz, “On Completeness of the-calculus", Proceedings of the 8th An-nual IEEE Symposium on Logic in Computer Science (LICS '93) (IEEE Computer Society Press, 1993); 136-146.
40. I. Walukiewicz, “A Note on the Completeness of Kozen's Axiomatization of the Propositonal-calculus", Bulletin of Symbolic Logic 2 (1996) 349-366.