On the power of real turing machines over binary inputs

SIAM Journal on Computing

Volumn 26, Issue 1, 1997, Pages 243-254

  Cucker, Felipe ^a   Grigoriev, Dima ^b  

^a UNIVERSITAT POMPEU FABRA   (Spain)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Complexity classes; Real number machines and computations

Indexed keywords

EID: 0001682069     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539794270340     Document Type: Article

References (29)

1. J. L. BALCÁZAR, J. DÍAZ, AND J. GABARRÓ, Structural Complexity I, EATCS Monographs on Theoretical Computer Science 11, Springer-Verlag, Berlin, 1988.
2. J. L. BALCÁZAR, J. DÍAZ, AND J. GABARRÓ, Structural Complexity II, EATCS Monographs on Theoretical Computer Science 22, Springer-Verlag, Berlin, 1990.
3. M. BEN-OR, Lower bounds for algebraic computation trees, in Proc. 15th ACM Symposium on the Theory of Computing, ACM, New York, 1983, pp. 80-86.
4. A. BERTONI, G. MAURI, AND N. SABADINI, Simulations among classes of random access machines and equivalence among numbers succinctly represented, Ann. Discrete Math., 25 (1985), pp. 65-90.
5. L. BLUM, M. SHUB, AND S. SMALE, On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines, Bull. Amer. Math. Soc., 21 (1989), pp. 1-46.
6. J. BOCHNAK, M. COSTE, AND M.-F. ROY, Géométrie algébrique réelle, Springer-Verlag, Berlin, 1987.
7. A. BORODIN, On relating time and space to size and depth, SIAM J. Comput., 6 (1977), pp. 733-744.
8. M. COSTE AND M.-F. ROY, Thom's lemma, the coding of real algebraic numbers and the topology of semi-algebraic sets, J. Symbolic Comput., 5 (1988), pp. 121-129.
9. IR, J. Complexity, 8 (1992), pp. 230-238.
10. F. CUCKER, On the complexity of quantifier elimination: The structural approach, Comput. J., 36 (1993), pp. 400-408.
11. F. CUCKER AND P. KOIRAN, Computing over the reals with addition and order: Higher complexity classes, J. Complexity, 11 (1995), pp. 358-376.
12. F. CUCKER, H. LANNEAU, B. MISHRA, P. PEDERSEN, AND M.-F. ROY, NC algorithms for real algebraic numbers, Appl. Algebra Engrg. Comm. Comput., 3 (1992), pp. 79-98.
13. F. CUCKER, M. SHUB, AND S. SMALE, Complexity separations in Koiran's weak model, Theoret. Comput. Sci., 133 (1994), pp. 3-14.
14. J. B. GOODE, Accessible telephone directories, J. Symbolic Logic, 59 (1994), pp. 92-105.
15. D. Y. GRIGORIEV, Complexity of deciding Tarski algebra, J. Symbolic Comput., 5 (1988), pp. 65-108.
16. D. Y. GRIGORIEV AND N. N. VOROBJOV, Solving systems of polynomial inequalities in subexponential time, J. Symbolic Comput., 5 (1988), pp. 37-64.
17. J. HEINTZ, T. KRICK, M.-F. ROY, AND P. SOLERNÓ, Geometric problems solvable in single exponential time, in Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes: Proc. 8th International Conference, S. Sakata, ed., Lecture Notes in Comput. Sci. 508, Springer-Verlag, Berlin, 1991, pp. 11-23.
18. J. HEINTZ, M.-F. ROY, AND P. SOLERNÓ, Sur la complexité du principe de Tarski-Seidenberg, Bull. Soc. Math. France, 118 (1980), pp. 101-126.
19. R. KARP AND R. LIPTON, Turing machines that take advice, Enseign. Math., 28 (1982), pp. 191-209.
20. P. KOIRAN, A weak version of the Blum, Shub and Smale model, in Proc. 34th Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1993, pp. 486-495.
21. P. KOIRAN, Computing over the reals with addition and order, Theoret. Comput. Sci., 133 (1994), pp. 35-47.
22. P. KOIRAN, A weak version of the Blum, Shub and Smale model. Technical report 94-10, DIMACS, Rutgers University, Piscataway, NJ, 1994.
23. W. MAASS, Bounds for the computational power and learning complexity of analog neural nets, in Proc. 25th Symposium on the Theory of Computing, ACM, New York, 1993, pp. 335-344.
24. J. MILNOR, Topology from the Differentialble Viewpoint, University Press of Virginia, Charlottesville, VA, 1965.
25. J. RENEGAR, On the computational complexity and geometry of the first-order theory of the reals, part III, J. Symbolic Comput., 13 (1992), pp. 329-352.
26. J. RENEGAR, On the computational complexity and geometry of the first-order theory of the reals, part I, J. Symbolic Comput., 13 (1992), pp. 255-299.
27. M.-F. ROY AND A. SZPIRGLAS, Complexity of computation on real algebraic numbers, J. Symbolic Comput., 7 (1990), pp. 39-51.
28. H. T. SIEGELMANN AND E. D. SONTAG, On the computational power of neural nets, in Proc. 5th ACM Workshop on Computational Learning Theory, ACM, New York, 1992, pp. 440-449.
29. H. T. SIEGELMANN AND E. D. SONTAG, Analog computation via neural networks, Theoret. Compot. Sci., 131 (1994), pp. 331-360.