메뉴 건너뛰기




Volumn 20, Issue 6, 2004, Pages 835-857

Real recursive functions and their heirarchy

Author keywords

Analog computation; General purpose analog computer; Recursive functions over the reals

Indexed keywords

ANALOG COMPUTERS; BESSEL FUNCTIONS; COMPUTATIONAL COMPLEXITY; DIFFERENTIAL EQUATIONS; GENERAL PURPOSE COMPUTERS; MATHEMATICAL MODELS;

EID: 10244239347     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jco.2004.06.001     Document Type: Article
Times cited : (30)

References (24)
  • 1
    • 0003615227 scopus 로고    scopus 로고
    • Complexity and Real Computation
    • Springer, Berlin
    • L. Blum, F. Cucker, M. Shub, S. Smale, Complexity and Real Computation, Springer, Berlin, 1998.
    • (1998)
    • Blum, L.1    Cucker, F.2    Shub, M.3    Smale, S.4
  • 2
  • 3
    • 84958742393 scopus 로고    scopus 로고
    • The complexity of real recursive functions
    • C.S. Calude, M.J. Dinneen, F. Peper (Eds.), UNIC 2002, Lecture Notes in Computer Science, Springer, Berlin
    • M.L. Campagnolo, The complexity of real recursive functions, C.S. Calude, M.J. Dinneen, F. Peper (Eds.), Unconventional Models of Computation, UNIC 2002, Lecture Notes in Computer Science, Vol. 2509, Springer, Berlin, 2002, pp. 1-14.
    • (2002) Unconventional Models of Computation , vol.2509 , pp. 1-14
    • Campagnolo, M.L.1
  • 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
    • 0000948377 scopus 로고    scopus 로고
    • Even Turing machines can compute uncomputable functions
    • C.S. Calude, J. Casti, M.J. Dinneen (Eds.), Springer, Berlin
    • B.J. Copeland, Even Turing machines can compute uncomputable functions, in: C.S. Calude, J. Casti, M.J. Dinneen (Eds.), Unconventional Models of Computation, Springer, Berlin, 1998.
    • (1998) Unconventional Models of Computation
    • Copeland, B.J.1
  • 7
    • 0003874621 scopus 로고
    • Upper and lower bounds, Kluwer Academic Publishers, Dordrecht
    • L.D. Kudryavtsev, Encyclopaedia of Mathematics, Upper and lower bounds, Kluwer Academic Publishers, Dordrecht, 1993.
    • (1993) Encyclopaedia of Mathematics
    • Kudryavtsev, L.D.1
  • 8
    • 0141615048 scopus 로고    scopus 로고
    • Analog computers and recursive functions over the reals
    • D. Graça, J.F. Costa, Analog computers and recursive functions over the reals, J. Complexity 19 (2003) 644-664.
    • (2003) J. Complexity , vol.19 , pp. 644-664
    • Graça, D.1    Costa, J.F.2
  • 9
    • 0141563264 scopus 로고    scopus 로고
    • Non-Turing computations via Malament Hogarth space-times
    • G. Etesi, I. Nemeti, Non-Turing computations via Malament Hogarth space-times, Internal. J. Theoret. Phys. 41(2002)341-370.
    • (2002) Internal. J. Theoret. Phys. , vol.41 , pp. 341-370
    • Etesi, G.1    Nemeti, I.2
  • 10
    • 0009949264 scopus 로고
    • Arithmetical predicates and quantifiers
    • S.K. Kleene, Arithmetical predicates and quantifiers, Trans. Amer. Math. Soc. 79 (1955) 312-340.
    • (1955) Trans. Amer. Math. Soc. , vol.79 , pp. 312-340
    • Kleene, S.K.1
  • 11
    • 0008854035 scopus 로고    scopus 로고
    • Closed-form analytic maps in one and two dimensions can simulate universal Turing machines
    • P. Koiran, C. Moore, Closed-form analytic maps in one and two dimensions can simulate universal Turing machines, Theoret. Comput. Sci. 210 (1) (1999) 217-223.
    • (1999) Theoret. Comput. Sci. , vol.210 , Issue.1 , pp. 217-223
    • Koiran, P.1    Moore, C.2
  • 12
    • 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
  • 13
    • 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
  • 14
    • 0037901174 scopus 로고    scopus 로고
    • μ-recursion and infinite limits
    • J. Mycka, μ-recursion and infinite limits, Theoret. Comput. Sci. 302 (2003) 123-133.
    • (2003) Theoret. Comput. Sci. , vol.302 , pp. 123-133
    • Mycka, J.1
  • 17
    • 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
  • 18
    • 0030260761 scopus 로고    scopus 로고
    • On the role ofmathernatics and mathematical knowledge in the invention of Vannevar Bush's early analog computers
    • S. Puchta, On the role ofmathernatics and mathematical knowledge in the invention of Vannevar Bush's early analog computers, IEEE Ann. History Comput. 18 (4) (1996) 49-59.
    • (1996) IEEE Ann. History Comput. , vol.18 , Issue.4 , pp. 49-59
    • Puchta, S.1
  • 19
    • 0030286377 scopus 로고    scopus 로고
    • Small universal Turing machines. Universal machines and computations
    • Y. Rogozhin, Small universal Turing machines. Universal machines and computations, Theoret. Comput. Sci. 168 (2) (1996) 215-240.
    • (1996) Theoret. Comput. Sci. , vol.168 , Issue.2 , pp. 215-240
    • Rogozhin, Y.1
  • 20
    • 38249030758 scopus 로고
    • Some mathematical limitations of the general-purpose analog computer
    • L.A. Rubel, Some mathematical limitations of the general-purpose analog computer, Adv. Appl. Math. 9 (1988) 22-34.
    • (1988) Adv. Appl. Math. , vol.9 , pp. 22-34
    • Rubel, L.A.1
  • 21
    • 38249005670 scopus 로고
    • The extended analog computer
    • L.A. Rubel, The extended analog computer, Adv. Appl. Math. 14 (1993) 39-50.
    • (1993) Adv. Appl. Math. , vol.14 , pp. 39-50
    • Rubel, L.A.1
  • 22
    • 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
  • 24
    • 0000721912 scopus 로고
    • The existence of noncollision singularities in Newtonian systems
    • Z. Xia, The existence of noncollision singularities in Newtonian systems, Ann. Math. 135 (3) (1992) 411-468.
    • (1992) Ann. Math. , vol.135 , Issue.3 , pp. 411-468
    • Xia, Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.