메뉴 건너뛰기




Volumn 317, Issue 1-3, 2004, Pages 115-145

Natural computation and non-Turing models of computation

Author keywords

Analog computation; Computation on reals; Continuous computation; Natural computation; Turing machine

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTATIONAL METHODS; COMPUTER SCIENCE; FORMAL LOGIC; FUNCTIONS; MATHEMATICAL TRANSFORMATIONS;

EID: 2442610829     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2003.12.008     Document Type: Conference Paper
Times cited : (67)

References (52)
  • 2
    • 84968516134 scopus 로고
    • On a theory of computation and complexity over the real numbers: NP completeness, recursive functions and universal machines
    • Blum L., Shub M., Smale S. On a theory of computation and complexity over the real numbers. NP completeness, recursive functions and universal machines Bull. Amer. Math. Soc. 21:1988;1-46.
    • (1988) Bull. Amer. Math. Soc. , vol.21 , pp. 1-46
    • Blum, L.1    Shub, M.2    Smale, S.3
  • 3
    • 2442564650 scopus 로고
    • Universal limit Turing machines
    • translated from Russian
    • Burgin M. Universal limit Turing machines. Notices Russian Acad. Sci. 325:1992;654-658. (translated from Russian).
    • (1992) Notices Russian Acad. Sci. , vol.325 , pp. 654-658
    • Burgin, M.1
  • 5
  • 7
    • 0021752535 scopus 로고
    • Spatial visual channels in the Fourier plane
    • Daugman J.G. Spatial visual channels in the Fourier plane. Vision Res. 24:1984;891-910.
    • (1984) Vision Res. , vol.24 , pp. 891-910
    • Daugman, J.G.1
  • 8
    • 0002435967 scopus 로고
    • An information-theoretic view of analog representation in striate cortex
    • E.L. Schwartz. Cambridge, MA: MIT Press
    • Daugman J.G. An information-theoretic view of analog representation in striate cortex. Schwartz E.L. Computational Neuroscience. 1985;403-423 MIT Press, Cambridge, MA.
    • (1985) Computational Neuroscience , pp. 403-423
    • Daugman, J.G.1
  • 9
    • 0022098435 scopus 로고
    • Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters
    • Daugman J.G. Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters. J. Opt. Soc. Amer. A. 2:1985;1160-1169.
    • (1985) J. Opt. Soc. Amer. A , vol.2 , pp. 1160-1169
    • Daugman, J.G.1
  • 10
    • 0024053929 scopus 로고
    • Complete 2-D gabor transforms by neural networks for image analysis and compression
    • Daugman J.G. Complete 2-D Gabor transforms by neural networks for image analysis and compression. IEEE Trans. Acoust. Speech Signal Process. 16:1988;1169-1179.
    • (1988) IEEE Trans. Acoust. Speech Signal Process. , vol.16 , pp. 1169-1179
    • Daugman, J.G.1
  • 12
    • 45149140937 scopus 로고
    • The symbol grounding problem
    • Harnad S. The symbol grounding problem. Physica D. 42:1990;335-346.
    • (1990) Physica D , vol.42 , pp. 335-346
    • Harnad, S.1
  • 13
    • 0001847982 scopus 로고
    • Grounding symbols in the analog world
    • Harnad S. Grounding symbols in the analog world. Think. 2:1993;12-78.
    • (1993) Think , vol.2 , pp. 12-78
    • Harnad, S.1
  • 14
    • 0003610914 scopus 로고
    • New York: Chelsea. (transl. J.R. Aumann)
    • Hausdorff F. Set Theory. 1957;Chelsea, New York. (transl. J.R. Aumann).
    • (1957) Set Theory
    • Hausdorff, F.1
  • 15
    • 0023561038 scopus 로고
    • Technology-independent design of neurocomputers: The universal field computer
    • M. Caudill, & C. Butler. New York: IEEE Press
    • MacLennan B.J. Technology-independent design of neurocomputers: the universal field computer. Caudill M., Butler C. Proc. IEEE 1st Internat. Conf. Neural Networks. Vol. 3:1987;39-49 IEEE Press, New York.
    • (1987) Proc. IEEE 1st Internat. Conf, Neural Networks , vol.3 , pp. 39-49
    • Maclennan, B.J.1
  • 16
  • 17
    • 0003650159 scopus 로고
    • Field computation: A theoretical framework for massively parallel analog computation, Parts I-IV
    • Department of Computer Science University of Tennessee, Knoxville
    • B.J. MacLennan, Field computation: a theoretical framework for massively parallel analog computation, Parts I-IV, Tech. Report CS-90-100, Department of Computer Science University of Tennessee, Knoxville, 1990. http://www.cs.utk. edu/~mclennan .
    • (1990) Tech. Report , vol.CS-90-100
    • Maclennan, B.J.1
  • 18
    • 0003997062 scopus 로고
    • Gabor representations of spatiotemporal visual images
    • Department of Computer Science, University of Tennessee, Knoxville
    • B.J. MacLennan, Gabor representations of spatiotemporal visual images, Tech. Report CS-91-144, Department of Computer Science, University of Tennessee, Knoxville, 1991. http://www.cs.utk.edu/~mclennan .
    • (1991) Tech. Report , vol.CS-91-144
    • Maclennan, B.J.1
  • 19
    • 0027591020 scopus 로고
    • Characteristics of connectionist knowledge representation
    • MacLennan B.J. Characteristics of connectionist knowledge representation. Inform. Sci. 70:1993;119-143. http://www.cs.utk.edu/~mclennan.
    • (1993) Inform. Sci. , vol.70 , pp. 119-143
    • Maclennan, B.J.1
  • 21
    • 0003130091 scopus 로고
    • Grounding analog computers
    • cogprints.soton.ac.uk/abs/comp/199906003
    • MacLennan B.J. Grounding analog computers. Think. 2:1993;48-51. http://www.cs.utk.edu/~mclennan or cogprints.soton.ac.uk/abs/comp/199906003.
    • (1993) Think , vol.2 , pp. 48-51
    • Maclennan, B.J.1
  • 22
    • 0013152041 scopus 로고
    • Continuous computation and the emergence of the discrete
    • K.H. Pribram. Hillsdale: Lawrence Erlbaum, cogprints.soton.ac.uk/abs/ comp/199906001
    • MacLennan B.J. Continuous computation and the emergence of the discrete. Pribram K.H. Origins: Brain & Self-Organization. 1994;121-151 Lawrence Erlbaum, Hillsdale. http://www.cs.utk.edu/~mclennan or cogprints.soton.ac.uk/ abs/comp/199906001.
    • (1994) Origins: Brain & Self-organization , pp. 121-151
    • Maclennan, B.J.1
  • 23
    • 0001823797 scopus 로고
    • Continuous symbol systems: The logic of connectionism
    • D.S. Levine, & M. Aparicio IV. Hillsdale: Lawrence Erlbaum.
    • MacLennan B.J. Continuous symbol systems: the logic of connectionism. Levine D.S., Aparicio IV M. Neural Networks for Knowledge Representation and Inference. 1994;83-120 Lawrence Erlbaum, Hillsdale. www.cs.utk.edu/~mclennan.
    • (1994) Neural Networks for Knowledge Representation and Inference , pp. 83-120
    • Maclennan, B.J.1
  • 24
    • 0001259139 scopus 로고
    • Words lie in our way
    • cogprints.soton.ac.uk/abs/phil/199906001
    • MacLennan B.J. Words lie in our way. Minds Mach. 4:1994;421-437. http://www.cs.utk.edu/~mclennan or cogprints.soton.ac.uk/abs/phil/199906001.
    • (1994) Minds Mach. , vol.4 , pp. 421-437
    • Maclennan, B.J.1
  • 26
    • 77956783759 scopus 로고    scopus 로고
    • Field computation in motor control
    • P.G. Morasso, & V. Sanguineti. Amsterdam: Elsevier.
    • MacLennan B.J. Field computation in motor control. Morasso P.G., Sanguineti V. Self-Organization, Computational Maps and Motor Control. 1997;37-73 Elsevier, Amsterdam. http://www.cs.utk.edu/~mclennan.
    • (1997) Self-organization, Computational Maps and Motor Control , pp. 37-73
    • Maclennan, B.J.1
  • 27
    • 0033207969 scopus 로고    scopus 로고
    • Field computation in natural and artificial intelligence
    • MacLennan B.J. Field computation in natural and artificial intelligence. Inform. Sci. 119:1999;73-89. http://www.cs.utk.edu/~mclennan.
    • (1999) Inform. Sci. , vol.119 , pp. 73-89
    • Maclennan, B.J.1
  • 28
    • 0013152484 scopus 로고    scopus 로고
    • Can differential equations compute?
    • Department of Computer Science, University of Tennessee, Knoxville
    • B.J. MacLennan, Can differential equations compute?, Tech. Report UT-CS-01-459, Department of Computer Science, University of Tennessee, Knoxville, 2001. http://www.cs.utk.edu/~mclennan
    • (2001) Tech. Report , vol.UT-CS-01-459
    • Maclennan, B.J.1
  • 29
    • 1642378817 scopus 로고    scopus 로고
    • Continuous information representation and processing in natural and artificial neural networks
    • Department of Computer Science, University of Tennessee, Knoxville
    • B.J. MacLennan, Continuous information representation and processing in natural and artificial neural networks, Tech. Report UT-CS-03-508, Department of Computer Science, University of Tennessee, Knoxville, 2003. http://www.cs.utk.edu/~mclennan
    • (2003) Tech. Report , vol.UT-CS-03-508
    • Maclennan, B.J.1
  • 30
    • 0037312518 scopus 로고    scopus 로고
    • Transcending turing computability
    • MacLennan B.J. Transcending Turing computability. Minds Mach. 13:2003;3-22. http://www.cs.utk.edu/~mclennan.
    • (2003) Minds Mach. , vol.13 , pp. 3-22
    • Maclennan, B.J.1
  • 31
    • 2442430528 scopus 로고
    • Theory of Algorithms
    • transl. by J.J. Schorr-Kon, PST Staff, US Department Comm. Ofc. Tech. Service OTS 60-51085, Jerusalem
    • A.A. Markov, Theory of Algorithms, transl. by J.J. Schorr-Kon, PST Staff, Israel Prog. Sci. Transl. US Department Comm. Ofc. Tech. Service OTS 60-51085, Jerusalem, 1961. (Transl. of Teoriya Algorifmov, Acad. Sci. USSR, Moscow, 1954).
    • (1961) Israel Prog. Sci. Transl.
    • Markov, A.A.1
  • 32
    • 2442478530 scopus 로고
    • Acad. Sci. USSR, Moscow
    • A.A. Markov, Theory of Algorithms, transl. by J.J. Schorr-Kon, PST Staff, Israel Prog. Sci. Transl. US Department Comm. Ofc. Tech. Service OTS 60-51085, Jerusalem, 1961. (Transl. of Teoriya Algorifmov, Acad. Sci. USSR, Moscow, 1954).
    • (1954) Transl. of Teoriya Algorifmov
  • 36
    • 0038907126 scopus 로고
    • Topology without points
    • Menger K. Topology without points. Rice Inst. Pamphlet. 27:1940;80-107.
    • (1940) Rice Inst. Pamphlet , vol.27 , pp. 80-107
    • Menger, K.1
  • 37
    • 0011600697 scopus 로고
    • Partially ordered sets, separating systems and inductiveness
    • Milgram A.N. Partially ordered sets, separating systems and inductiveness. Rep. Math. Colloq. Notre Dame Ind. 2nd Ser. 1:1939;18-30.
    • (1939) Rep. Math. Colloq. Notre Dame Ind. 2nd Ser. , vol.1 , pp. 18-30
    • Milgram, A.N.1
  • 39
    • 2442532974 scopus 로고
    • Partially ordered sets and topology
    • Milgram A.N. Partially ordered sets and topology. Proc. Natl. Acad. Sci. USA. 26:1940;291-293.
    • (1940) Proc. Natl. Acad. Sci. USA , vol.26 , pp. 291-293
    • Milgram, A.N.1
  • 40
    • 0030570631 scopus 로고    scopus 로고
    • Recursion theory on the reals and continuous-time computation
    • Moore C. Recursion theory on the reals and continuous-time computation. Theoret. Comput. Sci. 162:1996;23-44.
    • (1996) Theoret. Comput. Sci. , vol.162 , pp. 23-44
    • Moore, C.1
  • 43
    • 84967792518 scopus 로고
    • Abstract computability and its relation to the general purpose analog computer (Some connections between logic, differential equations and analog computers)
    • Pour-El M.B. Abstract computability and its relation to the general purpose analog computer (Some connections between logic, differential equations and analog computers). Trans. Amer. Math. Soc. 199:1974;1-29.
    • (1974) Trans. Amer. Math. Soc , vol.199 , pp. 1-29
    • Pour-El, M.B.1
  • 45
    • 84966203420 scopus 로고
    • A universal differential equation
    • Rubel L.A. A universal differential equation. Bull. (NS) Amer. Math. Soc. 4:1981;345-349.
    • (1981) Bull. (NS) Amer. Math. Soc. , vol.4 , pp. 345-349
    • Rubel, L.A.1
  • 46
    • 38249005670 scopus 로고
    • The extended analog computer
    • Rubel L.A. The extended analog computer. Adv. Appl. Math. 14:1993;39-50.
    • (1993) Adv. Appl. Math. , vol.14 , pp. 39-50
    • Rubel, L.A.1
  • 47
    • 85163157556 scopus 로고
    • Mathematical theory of the differential analyzer
    • Shannon C.E. Mathematical theory of the differential analyzer. J. Math. Phys. MIT. 20:1941;337-354.
    • (1941) J. Math. Phys. MIT , vol.20 , pp. 337-354
    • Shannon, C.E.1
  • 48
    • 0010621639 scopus 로고
    • Form, formation, and transformation of internal representations
    • R.L. Solso. Hillsdale: Lawrence Erlbaum
    • Shepard R.N. Form, formation, and transformation of internal representations. Solso R.L. Information Processing in Cognition: The Loyola Symposium. 1975;Lawrence Erlbaum, Hillsdale.
    • (1975) Information Processing in Cognition: The Loyola Symposium
    • Shepard, R.N.1
  • 49
    • 0015231889 scopus 로고
    • Mental rotation of three-dimensional objects
    • Shepard R.N., Metzler J. Mental rotation of three-dimensional objects. Science. 171:1971;701-703.
    • (1971) Science , vol.171 , pp. 701-703
    • Shepard, R.N.1    Metzler, J.2
  • 50
    • 84968486072 scopus 로고
    • The theory of representation for Boolean algebras
    • Stone M.H. The theory of representation for Boolean algebras. Trans. Amer. Math. Soc. 40:1936;37-111.
    • (1936) Trans. Amer. Math. Soc. , vol.40 , pp. 37-111
    • Stone, M.H.1
  • 51
    • 84968483087 scopus 로고
    • Applications of the theory of Boolean rings to general topology
    • Stone M.H. Applications of the theory of Boolean rings to general topology. Trans. Amer. Math. Soc. 41:1937;375-481.
    • (1937) Trans. Amer. Math. Soc. , vol.41 , pp. 375-481
    • Stone, M.H.1
  • 52
    • 0001759439 scopus 로고
    • Lattices and topological spaces
    • Wallman H. Lattices and topological spaces. Ann. Math. (Ser. 2). 39:1938;112-126.
    • (1938) Ann. Math. (Ser. 2) , vol.39 , pp. 112-126
    • Wallman, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.