Super-turing or non-turing? Extending the concept of computation

International Journal of Unconventional Computing

Volumn 5, Issue 3-4, 2009, Pages 369-387

  MacLennan, Bruce J ^a  

^a University of Tennessee Knoxville   (United States)

Author keywords

Church turing thesis; Hypercomputation; Model of computation; Nanocomputation; Natural computation; Non turing computation; Theory of computation; Turing computation

Indexed keywords

EID: 77952536424     PISSN: 15487199     EISSN: 15487202     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. A. Adamatzky. Computing in Nonlinear Media and Automata Collectives. Institute of Physics Publishing, Bristol & Philadelphia, 2001.
2. A. Adamatzky, B. De Lacy Costello and T. Asai. Reaction-Diffusion Computers. Elsevier, Amsterdam, 2005.
3. C.S. Calude, J. Casti and M.J. Dinneen, editors. Unconventional Models of Computation. Springer, Singapore & New York, 1998.
4. C.S. Calude and Gh. Pǎun. Computing with Cells and Atoms. Taylor & Francis, London & New York, 2001.
5. J.G. Daugman. An information-theoretic view of analog representation in striate cortex. In E. Schwartz, editor, Computational Neuroscience. MIT Press, Cambridge, 1985, pp. 403-423.
6. E. Eberbach, D. Goldin and P. Wegner. Turing's ideas and models of computation. In Ch. Teuscher, editor, Alan Turing: Life and Legacy of a Great Thinker. Springer-Verlag, Berlin, Heidelberg & New York, 2003.
7. S. Harnad. The symbol grounding problem. Physica D 42 (1990), 335-346.
8. S. Harnad. Grounding symbols in the analog world. Think 2 (1993), 12-78. Also Psycholoquy, 12(34) (2001).
9. S. Haykin. Neural Networks: A Comprehensive Foundation. Prentice Hall, Upper Saddle River, NJ, second edition, 1999.
10. W. Maass and E.D. Sontag. Analog neural nets with Gaussian or other common noise distributions cannot recognize arbitrary regular languages. Neural Computation 11 (1999), 771-782.
11. B.J. MacLennan. Technology-independent design of neurocomputers: The universal field computer. In M. Caudill and C. Butler, editors, Proceedings IEEE First International Conference on Neural Networks Volume 3, IEEE Press, 1987, pp. 39-49.
12. B.J. MacLennan. Grounding analog computers. Think 2 (1993), 48-51. Also Psycholoquy, 12(52) (2001).
13. B.J. MacLennan. Continuous symbol systems: The logic of connectionism. In D.S. Levine and M.Aparicio IV, editors, Neural Networks for Knowledge Representation and Inference, Lawrence Erlbaum, Hillsdale, pp. 83-120, 1994.
14. B.J. MacLennan. 'Words lie in our way'. Minds and Machines 4 (1994), 421-437.
15. B.J. MacLennan. Continuous formal systems: A unifying model in language and cognition. In Proceedings of the IEEE Workshop on Architectures for Semiotic Modeling and Situation Analysis in Large Complex Systems, IEEE. Monterey, CA, August 27-29, 1995, pp. 161-172.
16. B.J. MacLennan. Field computation in natural and artificial intelligence. Information Sciences 119 (1999), 73-89.
17. B.J. MacLennan. Transcending Turing computability. Minds and Machines 13(2003), 3-22.
18. B.J. MacLennan. Natural computation and non-Turing models of computation. Theoretical Computer Science 317(1-3) (2004), 115-145.
19. B.J. MacLennan. The U-machine: A model of generalized computation. Technical Report UT-CS-06-587, Department of Computer Science, University of Tennessee, Knoxville. Submitted for publication, 2006.
20. A.A. Markov. Theory of Algorithms. (1961). Israel Program for Scientific Translation, Jerusalem, Israel. US Dept. of Commerce Office of Technical Service OTS 60-51085, transl. by Jacques J. Schorr-Kon & PST Staff. Translation of Teoriya Algorifmov. Academy of Sciences of the USSR, Moscow, 1954.
21. R. Milner. Elements of interaction. Communications of the ACM 36(1) (1993), 78-89.
22. R. Milner, J. Parrow and D. Walker. Acalculus of mobile processes, I & II. Information and Computation 100 (1992), 1-77.
23. L.A. Rubel. The extended analog computer. Advances in Applied Mathematics 14 (1993), 39-50.
24. C. Shannon. Mathematical theory of the differential analyzer. Journal of Mathematics and Physics of the Massachusetts Institute Technology 20 (1941), 337-354.
25. H.T. Siegelmann and E.D. Sontag. Analog computation via neural networks. Theoretical Computer Science 131(2) (1994), 331-360.
26. D.A. Sprecher. On the structure of continuous functions of several variables. Transactions of the American Mathematical Society 115 (1965), 340-355.
27. P. Wegner. Why interaction is more powerful than algorithms. Communications of the ACM 40(5) (1997),81-91.
28. P. Wegner. Interactive foundations of computing. Theoretical Computer Science 192(2) (1998),315-351.
29. P. Wegner and D. Goldin. Computation beyond Turing machines: Seeking appropriate methods to model computing and human thought. Communications of the ACM 46 (4) (2003), 100-102.
30. E. Winfree. Algorithmic Self-Assembly of DNA. PhD thesis, California Institute of Technology, 1998.