메뉴 건너뛰기




Volumn 21, Issue 1, 1989, Pages 1-46

On a theory of computation and complexity over the real numbers: Np-completeness, recursive functions and universal machines

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84968516134     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0273-0979-1989-15750-9     Document Type: Article
Times cited : (805)

References (60)
  • 1
    • 0015201785 scopus 로고
    • Proceedings of the 12th Annual (IEEE) Symposium on Switching and Automata Theory
    • F. Abramson, Effective computation over the real numbers, Proceedings of the 12th Annual (IEEE) Symposium on Switching and Automata Theory, 1971, pp. 33–37
    • (1971) Effective Computation over the Real Numbers , pp. 33-37
    • Abramson, F.1
  • 3
    • 84968497743 scopus 로고
    • On the real spectrum of a ring and its application to semialgebraic geometry
    • E. Becker, On the real spectrum of a ring and its application to semialgebraic geometry, Bull. Amer. Math. Soc. (N.S.) 15 (1986), 19–60
    • (1986) Bull. Amer. Math. Soc. (N.S.) , vol.15 , pp. 19-60
    • Becker, E.1
  • 5
    • 84968494997 scopus 로고
    • Complex analytic dynamics of the Riemann sphere
    • P. Blanchard, Complex analytic dynamics of the Riemann sphere, Bull. Amer. Math. Soc. (N.S.) 11 (1984), 85–141
    • (1984) Bull. Amer. Math. Soc. (N.S.) , vol.11 , pp. 85-141
    • Blanchard, P.1
  • 6
    • 84909661317 scopus 로고
    • Logic and Algorithmic, Monographie, no. 30, de L’enseignement Mathematique, Geneva
    • A. Borodin, Structured vs. general models in computational complexity, Logic and Algorithmic, Monographie, no. 30, de L’enseignement Mathematique, Geneva, 1982, pp. 47–65
    • (1982) Structured Vs. General Models in Computational Complexity , pp. 47-65
    • Borodin, A.1
  • 7
    • 84950357804 scopus 로고
    • Invariant sets under iteration of rational functions
    • H. Brolin, Invariant sets under iteration of rational functions, Ark. Mat. 6 (1965) 103–144
    • (1965) Ark. Mat , vol.6 , pp. 103-144
    • Brolin, H.1
  • 10
    • 0003408347 scopus 로고
    • Cambridge Univ. Press, Cambridge
    • N. Cutland, Computability, Cambridge Univ. Press, Cambridge, 1980
    • (1980) Computability
    • Cutland, N.1
  • 12
    • 0001540194 scopus 로고
    • Hilbert’s tenth Problem. Diophantine equations: Positive aspects of a negative solution
    • Mathematical Development Arising from Hilbert Problems, Amer. Math. Soc., Providence, R.I
    • M. Davis, Y. Matijasevic, and J. Robinson, Hilbert’s tenth Problem. Diophantine equations: positive aspects of a negative solution, Mathematical Development Arising from Hilbert Problems, Proc. Sympos. Pure Math., vol. 28, Amer. Math. Soc., Providence, R.I., 1976, pp. 323–378
    • (1976) Proc. Sympos. Pure Math , vol.28 , pp. 323-378
    • Davis, M.1    Matijasevic, Y.2    Robinson, J.3
  • 13
    • 84972545546 scopus 로고
    • Diophantine sets over polynomial rings. III
    • M. Davis, and H. Putnam, Diophantine sets over polynomial rings. III, J. Math. 7 (1963), 251–256
    • (1963) J. Math , vol.7 , pp. 251-256
    • Davis, M.1    Putnam, H.2
  • 14
    • 84968507632 scopus 로고
    • 1, Diophantine sets over Z[T]
    • J. Denef, 1, Diophantine sets over Z[T], Proc. Amer. Math. Soc. 69 (1978), 148–150
    • (1978) Proc. Amer. Math. Soc , vol.69 , pp. 148-150
    • Denef, J.1
  • 15
    • 0001153514 scopus 로고
    • 2, The Diophantine problem for polynomial rings and fields of rational functions
    • J. Denef, 2, The Diophantine problem for polynomial rings and fields of rational functions, Trans. Amer. Math. Soc. 242 (1978), 391–399
    • (1978) Trans. Amer. Math. Soc , vol.242 , pp. 391-399
    • Denef, J.1
  • 18
    • 0015018320 scopus 로고
    • Algorithmic approximations
    • E. Engeler, Algorithmic approximations, J. Comput. System Sci. 5 (1971), 67–82
    • (1971) J. Comput. System Sci , vol.5 , pp. 67-82
    • Engeler, E.1
  • 20
    • 85012630262 scopus 로고
    • Computational complexity of real functions
    • H. Friedman and K. Ko, Computational complexity of real functions, J. Theoret. Comput. Sci. 20 (1982), 323–352
    • (1982) J. Theoret. Comput. Sci , vol.20 , pp. 323-352
    • Friedman, H.1    Ko, K.2
  • 23
    • 85025493187 scopus 로고
    • Solving systems of polynomial inequalities in subexponential time
    • 5 nos. 1 and 2
    • D. Y. Grigorev and N. N. Vorobojov, Solving systems of polynomial inequalities in subexponential time, J. Symbolic Computation, 5 nos. 1 and 2 (1988), 37–64
    • (1988) J. Symbolic Computation , pp. 37-64
    • Grigorev, D.Y.1    Vorobojov, N.N.2
  • 25
    • 0002984225 scopus 로고
    • Computability over arbitrary fields
    • G. T. Herman and S. D. Isard, Computability over arbitrary fields, J. London Math. Soc. (2) 2 (1970), 73–79
    • (1970) J. London Math. Soc , vol.2 , Issue.2 , pp. 73-79
    • Herman, G.T.1    Isard, S.D.2
  • 26
    • 0004211773 scopus 로고
    • Ph.D. Thesis, Department of Computer Science, Univ. of Toronto
    • H. J. Hoover, Feasibly constructive analysis, Ph.D. Thesis, Department of Computer Science, Univ. of Toronto, 1987
    • (1987) Feasibly Constructive Analysis
    • Hoover, H.J.1
  • 27
    • 0038160140 scopus 로고
    • Register machine proof of the theorem on exponential diophantine representation of enumerable sets
    • J. P. Jones and Y. V. Matijasevic, Register machine proof of the theorem on exponential diophantine representation of enumerable sets, J. Symbolic Logic 49 (1984), 818–829
    • (1984) J. Symbolic Logic , vol.49 , pp. 818-829
    • Jones, J.P.1    Matijasevic, Y.V.2
  • 29
    • 0020219723 scopus 로고
    • Complexity theory on real numbers and functions
    • Theoretical Computer Science, (A. B. Cremers and H. P. Kreigel eds.), Springer-Verlag, Berlin and New York
    • C. Kreitz and K. Weihrauch, Complexity theory on real numbers and functions, Lecture Notes in Computer Sci., 145, Theoretical Computer Science, (A. B. Cremers and H. P. Kreigel eds.), Springer-Verlag, Berlin and New York, 1982, pp. 165–174
    • (1982) Lecture Notes in Computer Sci , vol.145 , pp. 165-174
    • Kreitz, C.1    Weihrauch, K.2
  • 32
    • 0004248158 scopus 로고
    • Springer-Verlag, Berlin and New York, 1984 (2nd printing)
    • X. I. Manin, A course in mathematical logic, Springer-Verlag, Berlin and New York, 1977; 1984 (2nd printing)
    • (1977) A Course in Mathematical Logic
    • Manin, X.I.1
  • 35
    • 84966260816 scopus 로고
    • On the Betti-numbers of real varieties
    • J. Milnor, On the Betti-numbers of real varieties, Proc. Amer. Math. Soc. 15 (1964), 275–280
    • (1964) Proc. Amer. Math. Soc , vol.15 , pp. 275-280
    • Milnor, J.1
  • 38
    • 0000238829 scopus 로고
    • Methods of computing values of polynomials
    • V. Ya Pan, Methods of computing values of polynomials, Russian Math. Surveys 21 no. 1 (1966), 105–136
    • (1966) Russian Math. Surveys , vol.21 , Issue.1 , pp. 105-136
    • Ya Pan, V.1
  • 39
    • 0000664148 scopus 로고
    • Computability and noncomputability in classical analysis
    • M.B. Pour-Ei and I. Richards, Computability and noncomputability in classical analysis, Trans. Amer. Math. Soc. 275 (1983), 539–560
    • (1983) Trans. Amer. Math. Soc , vol.275 , pp. 539-560
    • Pour-Ei, M.B.1    Richards, I.2
  • 41
    • 84968513637 scopus 로고
    • Computable algebra, general theory and theory of computable fields
    • M. Rabin, 0.1, Computable algebra, general theory and theory of computable fields, Trans. Amer. Math. Soc. 95 (1960), 341–360
    • (1960) Trans. Amer. Math. Soc , vol.95 , pp. 341-360
    • Rabin, M.1
  • 42
    • 0015491021 scopus 로고
    • Proving simultaneous positivity of linear forms
    • 0.2
    • M. Rabin, 0.2, Proving simultaneous positivity of linear forms, J. Comput. and System Sci. 6 (1972), 639–650
    • (1972) J. Comput. and System Sci , vol.6 , pp. 639-650
    • Rabin, M.1
  • 43
    • 0024144944 scopus 로고
    • A faster PSPACE algorithm for deciding the existential theory of the reals
    • Technical Report No. 792, Cornell, April 1988. (Also, Proceedings. of the 29th Annual Symposium on Foundations of Computer Science
    • J. Renegar, A faster PSPACE algorithm for deciding the existential theory of the reals, Technical Report No. 792, School of Operations Research and Industrial Engineering, Cornell, April 1988. (Also, Proceedings. of the 29th Annual Symposium on Foundations of Computer Science, 1988, pp. 291–295.)
    • (1988) School of Operations Research and Industrial Engineering , pp. 291-295
    • Renegar, J.1
  • 45
    • 0038982373 scopus 로고
    • Factoring numbers in O(Log n) arithmetic steps
    • A. Shamir, Factoring numbers in O(log n) arithmetic steps, Inform. Process. Lett. 8 no. 1 (1979), 28–31
    • (1979) Inform. Process. Lett , vol.8 , Issue.1 , pp. 28-31
    • Shamir, A.1
  • 47
    • 85036616973 scopus 로고
    • Proc. 6th ICALP, Lecture Notes in Computer Science, Springer-Verlag, Berlin and New York
    • A. Schönhage, On the power of random access machines, Proc. 6th ICALP, Lecture Notes in Computer Science, no. 71, Springer-Verlag, Berlin and New York, 1979, pp. 520–529
    • (1979) On the Power of Random Access Machines , Issue.71 , pp. 520-529
    • Schönhage, A.1
  • 48
    • 45949121073 scopus 로고
    • On the topology of algorithms. I
    • S. Smale, On the topology of algorithms. I, J. Complexity 3 (1987), 81–89
    • (1987) J. Complexity , vol.3 , pp. 81-89
    • Smale, S.1
  • 50
    • 0002943521 scopus 로고
    • Lower bounds for algebraic decision trees
    • M. Steele and A. Yao, Lower bounds for algebraic decision trees, J. Algorithms 3 (1982), 1–8
    • (1982) J. Algorithms , vol.3 , pp. 1-8
    • Steele, M.1    Yao, A.2
  • 51
    • 0039916842 scopus 로고
    • Algebraische berechnungskomplexität
    • Basel), Birkhäuser-Verlag
    • V. Strassen, Algebraische berechnungskomplexität, Perspectives in Mathematics, (Basel), Birkhäuser-Verlag, 1984
    • (1984) Perspectives in Mathematics
    • Strassen, V.1
  • 52
    • 84968467211 scopus 로고    scopus 로고
    • Quasi-conformal homomorphisms and dynamics. III
    • preprint
    • D. Sullivan, Quasi-conformal homomorphisms and dynamics. III, IHES preprint
    • IHES
    • Sullivan, D.1
  • 54
    • 0002586126 scopus 로고
    • Sur l’homologie des variétés algébriques réelles
    • Princeton Univ. Press, Princeton, New Jersey
    • R. Thom, Sur l’homologie des variétés algébriques réelles, Differential and Combinatorial Topology, Princeton Univ. Press, Princeton, New Jersey, 1965, pp. 255–265
    • (1965) Differential and Combinatorial Topology , pp. 255-265
    • Thom, R.1
  • 55
    • 0003188711 scopus 로고
    • A survey of the logic of effective definitions
    • Logic of Programs, (E. Engeier, ed.), Springer-Verlag, Berlin New York
    • J. Tiuryn, A survey of the logic of effective definitions, Lecture Notes in Computer Sci., 125, Logic of Programs, (E. Engeier, ed.), Springer-Verlag, Berlin New York, 1979, pp. 198–245
    • (1979) Lecture Notes in Computer Sci , vol.125 , pp. 198-245
    • Tiuryn, J.1
  • 56
    • 0020116653 scopus 로고
    • Complexity of linear programming
    • J. F. Traub and H. Wozniakowski, Complexity of linear programming, Oper. Res. Lett. 1 no. 2, (1982), 59–62
    • (1982) Oper. Res. Lett , vol.1 , Issue.2 , pp. 59-62
    • Traub, J.F.1    Wozniakowski, H.2
  • 57
    • 85034715651 scopus 로고
    • Completeness classes in algebra
    • L. Valiant, Completeness classes in algebra, Proc. 11th Ann ACM STOC, 1979, pp. 249–261
    • (1979) Proc. 11th Ann ACM STOC , pp. 249-261
    • Valiant, L.1
  • 58
    • 0002546815 scopus 로고
    • Alfred Tarski’s elimination theory for real closed fields
    • L. van den Dries, Alfred Tarski’s elimination theory for real closed fields, J. Symbolic Logic 1 (1988), 7–19
    • (1988) J. Symbolic Logic , vol.1 , pp. 7-19
    • Van Den Dries, L.1
  • 59
    • 84910847209 scopus 로고
    • Technical Report No. 207/88, Department of Computer Science, University of Toronto, January
    • J. von zur Gathen, Algebraic complexity theory, Technical Report No. 207/88, Department of Computer Science, University of Toronto, January 1988, 37 pp
    • (1988) Algebraic Complexity Theory , pp. 37
    • Von Zur Gathen, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.