Abstract
We investigate the concept of generalised computability of operators and functionals de.ned on the set of continuous functions, firstly introduced in [9]. By working in the reals, with equality and without equality, we study properties of generalised computable operators and functionals. Also we propose interesting applications to formalisation of hybrid systems. We obtain some class of hybrid systems, which trajectories are computable in the sense of computable analysis.
This research was supported in part by the RFBR (grants N 99-01-00485, N 00-01- 00810) and by the Siberian Branch of RAS (a grant for young researchers, 2000)
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References
J. Barwise, Admissible sets and structures, Berlin, Springer-Verlag, 1975.
A. Edalat, P. Sünderhauf, A domain-theoretic approach to computability on the real line, Theoretical Computer Science, 210, 1998, pages 73–98.
Yu. L. Ershov, Definability and computability, Plenum, New York, 1996.
A. Grzegorczyk, On the definitions of computable real continuous functions, Fund. Math., N 44, 1957, pages 61–71.
T.A. Henzinger, Z. Manna, A. Pnueli, Towards refining Temporal Specifications into Hybrid Systems, LNCS N 736, 1993, pages 36–60.
M. Korovina, O. Kudinov, A New Approach to Computability over the Reals, SibAM, v. 8, N 3, 1998, pages 59–73.
M. Korovina, O. Kudinov, Characteristic Properties of Majorant-Computability over the Reals, Proc. of CSL’98, LNCS, 1584, 1999, pages 188–204.
M. Korovina, O. Kudinov, A Logical approach to Specifications of Hybrid Systems, Proc. of PSI’99, LNCS 1755, 2000, pages 10–16.
M. Korovina, O. Kudinov, Formalisation of Computability of Operators and Real-Valued Functionals via Domain Theory, Proceedings of CCA-2000, to appear in LNCS, 2001.
Z. Manna, A. Pnueli, Verifying Hybrid Systems, LNCS N 736, 1993, pages 4–36.
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.
A. Nerode, W. Kohn, Models for Hybrid Systems, Automata, Topologies, Controllability, Observability, LNCS N 736, 1993, pages 317–357.
W. Kohn, A. Nerode, J. B. Remmel Agent Based Velocity Control of Highway Systems, LNCS N 1273, 1997, pages 174–215.
M. B. Pour-El, J. I. Richards, Computability in Analysis and Physics, Springer-Verlag, 1988.
D. Scott, Outline of a mathematical theory of computation, In 4th Annual Princeton Conference on Information Sciences and Systems, 1970, pages 169–176.
Viggo Stoltenberg-Hansen, John V. Tucker, Concrete models of computation for topological algebras, TCS 219, 1999, pages 347–378.
K. Weihrauch, Computable analysis. An introduction, Springer, 2000.
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Korovina, M.V., Kudinov, O.V. (2001). Generalised Computability and Applications to Hybrid Systems. In: Bjørner, D., Broy, M., Zamulin, A.V. (eds) Perspectives of System Informatics. PSI 2001. Lecture Notes in Computer Science, vol 2244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45575-2_47
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DOI: https://doi.org/10.1007/3-540-45575-2_47
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