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Volumn 19, Issue 5, 2003, Pages 644-664

Analog computers and recursive functions over the reals

Author keywords

Analog circuits; Differentially algebraic functions; Recursive functions over the reals; Shannon's general purpose analog computer

Indexed keywords


EID: 0141615048     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0885-064X(03)00034-7     Document Type: Article
Times cited : (97)

References (15)
  • 1
    • 0001089886 scopus 로고
    • The differential analyzer. A new machine for solving differential equations
    • V. Bush, The differential analyzer. A new machine for solving differential equations, J. Franklin Inst. 212 (1931) 447-488.
    • (1931) J. Franklin Inst. , vol.212 , pp. 447-488
    • Bush, V.1
  • 3
    • 0141815143 scopus 로고    scopus 로고
    • Upper and lower bounds on continuous-time computation
    • I. Antoniou, C.S. Calude, M.J. Dinneen (Eds.), UMC'2K, DMTCS, Springer, Berlin
    • M.L. Campagnolo, C. Moore, Upper and lower bounds on continuous-time computation, in: I. Antoniou, C.S. Calude, M.J. Dinneen (Eds.), Unconventional Models of Computation, UMC'2K, DMTCS, Springer, Berlin, 2001, pp. 135-153.
    • (2001) Unconventional Models of Computation , pp. 135-153
    • Campagnolo, M.L.1    Moore, C.2
  • 4
    • 0011287661 scopus 로고    scopus 로고
    • Iteration, inequalities, and differentiability in analog computers
    • M.L. Campagnolo, C. Moore, J.F. Costa, Iteration, inequalities, and differentiability in analog computers, J. Complexity 16 (4) (2000) 642-660.
    • (2000) J. Complexity , vol.16 , Issue.4 , pp. 642-660
    • Campagnolo, M.L.1    Moore, C.2    Costa, J.F.3
  • 5
    • 0036889222 scopus 로고    scopus 로고
    • An analog characterization of the Grzegorczyk hierarchy
    • M.L. Campagnolo, C. Moore, J.F. Costa, An analog characterization of the Grzegorczyk hierarchy, J. Complexity 18 (4) (2002) 977-1000.
    • (2002) J. Complexity , vol.18 , Issue.4 , pp. 977-1000
    • Campagnolo, M.L.1    Moore, C.2    Costa, J.F.3
  • 6
    • 0141591957 scopus 로고    scopus 로고
    • The general purpose analog computer and recursive functions over the reals
    • M.Sc. Thesis, IST/UTL, (available online at)
    • D.S. Graça, The general purpose analog computer and recursive functions over the reals, M.Sc. Thesis, IST/UTL, 2002 (available online at http://w3.ualg.pt/~dgraca).
    • (2002)
    • Graça, D.S.1
  • 7
    • 0004220560 scopus 로고    scopus 로고
    • 8th Printing, Springer, Berlin
    • T.W. Hungerford, Algebra, 8th Printing, Springer, Berlin, 1996.
    • (1996) Algebra
    • Hungerford, T.W.1
  • 8
    • 0028496407 scopus 로고
    • Computability with low-dimensional dynamical systems
    • P. Koiran, M. Cosnard, M. Garzon, Computability with low-dimensional dynamical systems, Theoret. Comput. Sci. 132 (1994) 113-128.
    • (1994) Theoret. Comput. Sci. , vol.132 , pp. 113-128
    • Koiran, P.1    Cosnard, M.2    Garzon, M.3
  • 9
    • 84968510156 scopus 로고
    • A differentially algebraic replacement theorem, and analog computation
    • L. Lipshitz, L.A. Rubel, A differentially algebraic replacement theorem, and analog computation, Proc. Amer. Math. Soc. 99 (2) (1987) 367-372.
    • (1987) Proc. Amer. Math. Soc. , vol.99 , Issue.2 , pp. 367-372
    • Lipshitz, L.1    Rubel, L.A.2
  • 10
    • 0001102743 scopus 로고
    • Unpredictability and undecidability in dynamical systems
    • C. Moore, Unpredictability and undecidability in dynamical systems, Phys. Rev. Lett. 64 (1990) 2354-2357.
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 2354-2357
    • Moore, C.1
  • 11
    • 0030570631 scopus 로고    scopus 로고
    • Recursion theory on the reals and continuous-time computation
    • C. Moore, 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
  • 12
    • 84967792518 scopus 로고
    • Abstract computability and its relations to the general purpose analog computer
    • M.B. Pour-El, Abstract computability and its relations to the general purpose analog computer, Trans. Amer. Math. Soc. 199 (1974) 1-28.
    • (1974) Trans. Amer. Math. Soc. , vol.199 , pp. 1-28
    • Pour-El, M.B.1
  • 13
    • 85163157556 scopus 로고
    • Mathematical theory of the differential analyzer
    • C. Shannon, 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.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.