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International Andrei Ershov Memorial Conference on Perspectives of System Informatics

PSI 1999: Perspectives of System Informatics pp 10–16Cite as

A Logical Approach to Specification of Hybrid Systems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1755))

Abstract

The main subject of our investigation is behaviour of the continuous components of hybrid systems. By a hybrid system we mean a network of digital and analog devices interacting at discrete times. A first-order logical formalization of hybrid systems is proposed in which the trajectories of the continuous components are presented by majorant-computable functionals.

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References

  1. J. Backus, Can Programming be Liberated from the von Neumann Style, A Functional Style and its Algebra of Programs, Comm. of the ACM, V. 21, N 8, 1978, pages 613–642.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. Barwise, Admissible sets and structures, Berlin, Springer-Verlag, 1975.

    MATH  Google Scholar 

  3. L. Blum and M. Shub and S. Smale, On a theory of computation and complexity over the reals:NP-completeness, recursive functions and universal machines, Bull. Amer. Math. Soc., (N.S.), v. 21, no. 1, 1989, pages 1–46.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Edalat, P. Sünderhauf, A domain-theoretic approach to computability on the real line, Theoretical Computer Science. To appear.

    Google Scholar 

  5. Yu. L. Ershov, Definability and computability, Plenum, New York, 1996.

    Google Scholar 

  6. H. Freedman and K. Ko, Computational complexity of real functions, Theoret. Comput. Sci., v. 20, 1982, pages 323–352.

    Article  MathSciNet  Google Scholar 

  7. A Logical for specification of Continuous System, LNCS N 1386, 1998, pages 143–159.

    Google Scholar 

  8. S.S. Goncharov, D.I. Sviridenko, Σ-programming, Vychislitel’nye Sistemy, Novosibirsk, v. 107, 1985, pages 3–29.

    MATH  MathSciNet  Google Scholar 

  9. A. Grzegorczyk, On the definitions of computable real continuous functions, Fund. Math., N 44, 1957, pages 61–71.

    MATH  MathSciNet  Google Scholar 

  10. T.A. Henzinger, Z. Manna, A. Pnueli, Towards refining Temporal Specifications into Hybrid Systems, LNCS N 736, 1993, pages 36–60.

    Google Scholar 

  11. T.A. Henzinger, V. Rusu, Reachability Verification for Hybrid Automata, LNCS N 1386, 1998, pages 190–205.

    Google Scholar 

  12. M. Korovina, Generalized computability of real functions, Siberian Advance of Mathematics, v. 2, N 4, 1992, pages 1–18.

    MathSciNet  Google Scholar 

  13. M. Korovina, O. Kudinov, A New Approach to Computability over the Reals, SibAM, v. 8, N 3, 1998, pages 59–73.

    MATH  MathSciNet  Google Scholar 

  14. M. Korovina, O. Kudinov, Characteristic Properties of Majorant-Computability over the Reals, Proc. of CSL’98, LNCS, to appear.

    Google Scholar 

  15. C. Livadas, N.A. Lynch, Formal verification of Safety-Critical hybrid systems, LNCS N 1386, 1998, pages 253–273.

    Google Scholar 

  16. Z. Manna, A. Pnueli, Verifying Hybrid Systems, LNCS N 736, 1993, pages 4–36.

    Google Scholar 

  17. R. Montague, Recursion theory as a branch of model theory, Proc. of the third international congr. on Logic, Methodology and the Philos. of Sc., 1967, Amsterdam, 1968, pages 63–86.

    Google Scholar 

  18. Y. N. Moschovakis, Abstract first order computability, Trans. Amer. Math. Soc., v. 138, 1969, pages 427–464.

    Article  MATH  MathSciNet  Google Scholar 

  19. A. Nerode, W. Kohn Models for Hybrid Systems: Automata, Topologies, Controllability, Observability, LNCS N 736, 1993, pages 317–357.

    Google Scholar 

  20. M. B. Pour-El, J. I. Richards, Computability in Analysis and Physics, Springer-Verlag, 1988.

    Google Scholar 

  21. D. Scott, Outline of a mathematical theory of computation, In 4th Annual Princeton Conference on Information Sciences and Systems, 1970, pages 169–176.

    Google Scholar 

  22. V. Stoltenberg-Hansen and J. V. Tucker, Effective algebras, Handbook of Logic in computer Science, v. 4, Clarendon Press, 1995, pages 375–526.

    MathSciNet  Google Scholar 

  23. B.A. Trakhtenbrot, Yu. Barzdin, Finite automata: Behaviour and Syntheses, North-Holland, 1973.

    Google Scholar 

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Author information

Authors and Affiliations

  1. A. P. Ershov Institute of Informatics Systems, Acad. Lavrent’ev pr., 6, Novosibirsk, Russia

    Margarita V. Korovina

  2. Institute of Mathematics, University pr., 4, Novosibirsk, Russia

    Oleg V. Kudinov

Authors
  1. Margarita V. Korovina
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  2. Oleg V. Kudinov
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Editor information

Editors and Affiliations

  1. Department of Information Technology, Technical University of Denmark, Bldg. 244, 2800, Lyngby, Denmark

    Dines Bjøner

  2. Computer Science Department, Technical University of Munich, Arcisstr. 21, 80290, Munich, Germany

    Manfred Broy

  3. A.P. Ershov Institute of Informatics Systems, av. Ac. Lavrentyev 6, Novosibirsk, 630090, Russia

    Alexandre V. Zamulin

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© 2000 Springer-Verlag Berlin Heidelberg

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Korovina, M.V., Kudinov, O.V. (2000). A Logical Approach to Specification of Hybrid Systems. In: Bjøner, D., Broy, M., Zamulin, A.V. (eds) Perspectives of System Informatics. PSI 1999. Lecture Notes in Computer Science, vol 1755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46562-6_2

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  • DOI: https://doi.org/10.1007/3-540-46562-6_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67102-2

  • Online ISBN: 978-3-540-46562-1

  • eBook Packages: Springer Book Archive

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