Decidability and universality in symbolic dynamical systems

Fundamenta Informaticae

Volumn 74, Issue 4, 2006, Pages 463-490

  Delvenne, Jean Charles ^a   Krka, Petr ^b   Blondel, Vincent ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b CHARLES UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

CODES (SYMBOLS); COMPUTATIONAL METHODS; DECISION THEORY; DISCRETE TIME CONTROL SYSTEMS; DYNAMIC PROGRAMMING; TURING MACHINES;

CELLULAR AUTOMATA; COMPUTATIONAL UNIVERSALITY; DYNAMICAL SYSTEMS; PHYSICAL REALIZABILITY;

COMPUTABILITY AND DECIDABILITY;

EID: 33845529532     PISSN: 01692968     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (40)

1. E. Asarin and A. Bouajjani. Perturbed turing machines and hybrid systems. In Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science (LICS-01), pages 269-278, Los Alamitos, CA, June 16-19 2001. IEEE Computer Society.
2. E. Asarin, O. Maler, and A. Pnueli. Reachability analysis of dynamical systems having piecewise-constant derivatives. Theoretical Computer Science, 138(1):35-65, 1995. Special issue on hybrid systems.
3. J. Banks, J. Brooks, G. Cairns, G. Davis, and P. Stacey. On Devaney's definition of chaos. American Mathematics Monthly, 99:332-334, 1992.
4. A. Ben-Hur, H. T. Siegelmann, and S. Fishman. A theory of complexity for continuous time systems. Journal of Complexity, 18(1):51-86, 2002.
5. O. Bournez and M. Cosnard. On the computational power of dynamical systems and hybrid systems. Theoretical Computer Science, 168:417-459, 1996.
6. J. H. Conway. Unpredictable iterations. In Proceedings of the Number Theory Conference (Univ. Colorado, Boulder, Colo., 1972), pages 49-52, Boulder, Colo., 1972. Univ. Colorado.
7. J. P. Crutchfield and K. Young. Computation at the onset of chaos. In W. Zurek, editor, Complexity, Entropy and the Physics of Information, pages 223-269. Addison-Wesley, 1989.
8. M. D. Davis. A note on universal Turing machines. In C.E. Shannon and J. McCarthy, editors, Automata Studies, pages 167-175. Princeton University Press, 1956.
9. J.-C. Delvenne and V. D. Blondel. Quasiperiodic configurations and undecidable dynamics for tilings, infinite words and Turing machines. Theoretical Computer Science, 319:127-143, 2004.
10. J.-Ch. Delvenne, P. Kůrka, and V. D. Blondel. Computational universality in symbolic dynamical systems. In M. Margenstern, editor, MCU 2004, number 3354 in Lecture Notes in Computer Science, pages 104-115. Springer-Verlag, 2005.
11. R. Devaney. An Introduction to Chaotic Dynamical Systems. Addison-Wesley, 1989.
12. B. Durand and Z. Róka. The Game of Life: universality revisited. In M. Delorme and J. Mazoyer, editors, Cellular Automata: a Parallel Model, volume 460 of Mathematics and its Applications, pages 51-74. Kluwer Academic Publishers, 1999.
13. Edward Fredkin and Tommaso Toffoli. Conservative logic. International Journal of Theoretical Physics, 21(3-4):219-253, 1981/82. Physics of computation, Part 1 (Dedham, Mass., 1981).
14. Peter Gács. Reliable cellular automata with self-organization. In 38th Annual Symposium on Foundations of Computer Science, pages 90-99, Miami Beach, Florida, 20-22 October 1997. IEEE.
15. E. M. Clarke Jr., O. Grumberg, and D. A. Peled. Model checking. MIT Press, 1999.
16. H. Rogers Jr. Theory of recursive functions and effective computability. MIT Press, Cambridge, MA, second edition, 1987.
17. R. Kaivola. Using automata to characterise fixed point temporal logics. PhD thesis, University of Edinburgh, 1996.
18. P. Koiran. A family of universal recurrent networks. Theoretical Computer Science, 168(2):473-480, 1996. Universal machines and computations (Paris, 1995).
19. P. Koiran, M. Cosnard, and M. Garzon. Computability with low-dimensional dynamical systems. Theoretical Computer Science, 132(1-2):113-128, 1994.
20. P. Koiran and Cr. Moore. Closed-form analytic maps in one and two dimensions can simulate universal Turing machines. Theoretical Computer Science, 210(1):217-223, 1999.
21. P. Kůrka. On topological dynamics of Turing machines. Theoretical Computer Science, 174(1-2):203-216, 1997.
22. P. Kůrka. Zero-dimensional dynamical systems, formal languages, and universality. Theory of Computing Systems, 32(4):423-433, 1999.
23. P. Kůrka. Topological and Symbolic Dynamics, volume 11 of Cours Spécialisés. Société Mathématique de France, 2003.
24. C. G. Langton. Computation at the edge of chaos. Physica D, 42:12-37, 1990.
25. W. Maass and P. Orponen. On the effect of analog noise in discrete-time analog computations. Neural Computation, 10(5):1071-1095, 1998.
26. M. L. Minsky. Recursive unsolvability of Post's problem of "tag" and other topics in theory of Turing machines. Annals of Mathematics (2), 74:437-455, 1961.
27. M. Mitchell, P. T. Hraber, and J. P. Crutchfield. Dynamic computation, and the "edge of chaos": A reexamination. In G. Cowan, D. Pines, and D. Melzner, editors, Complexity: Metaphors, Models, and Reality, Santa Fe Institute Proceedings, Volume 19, pages 497-513. Addison-Wesley, 1994. Santa Fe Institute Working Paper 93-06-040.
28. Cr. Moore. Unpredictability and undecidability in dynamical systems. Physical Review Letters, 64(20):2354-2357, 1990.
29. Cr. Moore. Generalized shifts: Unpredictability and undecidability in dynamical systems. Nonlinearity, 4:199-230, 1991.
30. Cr. Moore. Dynamical recognizers: real-time language recognition by analog computers. Theoretical Computer Science, 201:99-136, 1998.
31. Cr. Moore. Finite-dimensional analog computers: Flows, maps, and recurrent neural networks. In C.S. Calude, J. Casti, and M. J. Dinneen, editors, Unconventional Models of Computation. Springer-Verlag, 1998.
32. P. Orponen. A survey of continuous-time computation theory. In D.-Z. Du and K.-I Ko, editors, Advances in Algorithms, Languages, and Complexity, pages 209-224. Kluwer Academic Publishers, 1997.
33. D. Perrin and J.-E. Pin. Infinite Words (Automata, Semigroups, Logic and Games), volume 141 of Pure and Applied Mathematics. Elsevier, 2004.
34. H. T. Siegelmann. Neural Networks and Analog Computation: Beyond the Turing Limit. Progress in Theoretical Computer Science. Springer-Verlag, 1999.
35. H. T. Siegelmann and S. Fishman. Analog computation with dynamical systems. Physica D, 120:214-235, 1998.
36. K. Sutner. Cellular automata and intermediate degrees. Theoretical Computer Science, 296(2):365-375, 2003.
37. K. Sutner. Universality and cellular automata. In M. Margenstern, editor, MCU 2004, number 3354 in Lecture Notes in Computer Science, pages 50-59. Springer-Verlag, 2005.
38. A. M. Turing. On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, 42(2):230-265, 1936.
39. K. Weihrauch. Computable Analysis. Springer-Verlag, 2000.
40. S. Wolfram. A new kind of science. Wolfram Media, Inc., Champaign, IL, 2002.