Undecidable event detection problems for ODEs of dimension one and two

Keijo Ruohonen

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (1997)

  • Volume: 31, Issue: 1, page 67-79
  • ISSN: 0988-3754

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Ruohonen, Keijo. "Undecidable event detection problems for ODEs of dimension one and two." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 31.1 (1997): 67-79. <http://eudml.org/doc/92554>.

@article{Ruohonen1997,
author = {Ruohonen, Keijo},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {Turing machines},
language = {eng},
number = {1},
pages = {67-79},
publisher = {EDP-Sciences},
title = {Undecidable event detection problems for ODEs of dimension one and two},
url = {http://eudml.org/doc/92554},
volume = {31},
year = {1997},
}

TY - JOUR
AU - Ruohonen, Keijo
TI - Undecidable event detection problems for ODEs of dimension one and two
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 1997
PB - EDP-Sciences
VL - 31
IS - 1
SP - 67
EP - 79
LA - eng
KW - Turing machines
UR - http://eudml.org/doc/92554
ER -

References

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  2. 2. P. HARTMAN, Ordinary Differential Equations. Birkhäuser, 1982. MR658490
  3. 3. J. E. HOPCROFT and J. D. ULLMAN, Introduction to Automata Theory, Languages and Computation. Addison-Wesley, 1979. Zbl0426.68001MR645539
  4. 4. P. KOIRAN, P. COSNARD and M. GARZON, Computability with Low-Dimensional Dynamical Systems. Theoret Comput. Sci. 132, 1994, pp. 113-128. Zbl0821.68053MR1290538
  5. 5. C. MOORE, Unpredictability and Undecidability in Dynamical Systems. Phys. Rev. Lett. 64, 1990, pp. 2354-2357. Zbl1050.37510MR1050259
  6. 6. C. MOORE, Generalized Shifts: Unpredictability and Undecidability in Dynamical Systems. Nonlinearity 4, 1991, pp. 199-230. Zbl0725.58013MR1107005
  7. 7. M. Y. LECERF, Machines de Turing réversibles. Récursive insolubilité en n ∈ N de l'équation u = θnu, où θ est un "isomorphisme de codes". Comptes Rendus 257, 1963, pp. 2597-2600. Zbl0192.06901MR175790
  8. 8. M. B. POUR-EL and I. RICHARDS, A Computable Ordinary Differential Equation which Possesses No Computable Solutions. Ann. Math. Logic 17, 1979, pp. 61-90. Zbl0424.68028MR552416
  9. 9. M. B. POUR-EL and I. RICHARDS, Computability in Analysis and Physics. Springer-Verlag, 1989. Zbl0678.03027MR1005942
  10. 10. E. O. ROXIN, Ordinary Differential Equations. Wadsworth, 1972. Zbl0255.34001MR463536
  11. 11. K. RUOHONEN, Undecidability of Event Detection for ODEs. J. Inform. Proc. Cybern. EIK, 29, 1993, pp. 101-113. Zbl0771.65035
  12. 12. K. RUOHONEN, Event Detection and Nonrecursive Hierarchies. Results and Trends in Theoretical Computer Science (J. Karhumäki, H. Maurer and G. Rozenberg, Eds.). Lecture Notes in Computer Science 812. Springer-Verlag, 1994, pp. 358-371. MR1286976
  13. 13. K. RUOHONEN, Decidability and Complexity of Event Detection Problems for ODEs. To appear in Complexity. Zbl0878.68062MR1473602
  14. 14. K. RUOHONEN, Reversible Machines and Post's Correspondence Problem for Biprefix Morphisms. Elektron. Inf.verarb. Kybern. EIK 21, 1985, pp. 579-595. Zbl0604.68057MR825861
  15. 15. L. F. SHAMPINE, I. GLADWELL and R. W. BRANKIN, Reliable Solution of Special Event Location Problems for ODEs. ACM Trans. Math. Software 17, 1991, pp. 11-25. Zbl0900.65208MR1103624
  16. 16. H. T. STEGELMANN, Computation Beyond the Turing Limit. Science 268, 1995, pp. 545-548. 

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