The General Purpose Analog Computer and Computable Analysis are Two Equivalent Paradigms of Analog Computation, Lecture Notes in Computer Science, vol.3959, pp.631-643, 2006. ,
DOI : 10.1007/11750321_60
URL : https://hal.archives-ouvertes.fr/inria-00102946
Universal computation and other capabilities of hybrid and continuous dynamical systems, Theoretical Computer Science, vol.138, issue.1, pp.67-100, 1995. ,
On a theory of computation and complexity over the real numbers: $NP$- completeness, recursive functions and universal machines, Bulletin of the American Mathematical Society, vol.21, issue.1, pp.1-46, 1989. ,
DOI : 10.1090/S0273-0979-1989-15750-9
Campagnolo ? « Computational complexity of real valued recursive functions and analog circuits, Thèse de doctorat, 2001. ,
Upper and lower bounds on continuous-time computation, 2nd International Conference on Unconventional Models of Computation -UMC'2K (I. Antoniou, C. Calude et M. Dinneen, pp.135-153, 2001. ,
Cristopher Moore et José Félix Costa ? « An analog characterization of the subrecursive functions, 4th Conference on Real Numbers and Computers (P. Kornerup, pp.91-109, 2000. ,
inequalities, and differentiability in analog computers, Journal of Complexity, vol.16, issue.4, pp.642-660, 2000. ,
Campagnolo et Kerry Ojakian ? « The methods of approximation and lifting in real computation, Third International Conference on Computability and Complexity in Analysis, 2006. ,
Observability of Piecewise-Affine Hybrid Systems, Lecture Notes in Computer Science, vol.2993, pp.265-279, 2004. ,
DOI : 10.1007/978-3-540-24743-2_18
Abstract geometrical computation : Turing-computing ability and undecidability, CiE Lecture Notes in Computer Science, vol.3526, pp.106-116, 2005. ,
José Félix Costa ? « Analog computers and recursive functions over the reals », Journal of Complexity, vol.19, issue.5, pp.644-664, 2003. ,
Campagnolo et Jorge Buescu ? « Robust simulations of Turing machines with analytic maps and flows, CiE Lecture Notes in Computer Science, vol.3526, pp.169-179, 2005. ,
Some recent developments on Shannon's General Purpose Analog Computer, Mathematical Logic Quarterly, vol.50, issue.4-5, pp.473-485, 2004. ,
On the definitions of computable real continuous functions, Fundamenta Mathematicae, vol.44, issue.1, pp.61-71, 1957. ,
DOI : 10.4064/fm-44-1-61-71
The ordinary differential equation defined by a computable function whose maximal interval of existence is non-computable, 7th Conference on Real Numbers and Computers (RNC 7), 2006. ,
Hogarth ? « Does general relativity allow an observer to view an eternity in a finite time ?, Foundations of Physics Letters, vol.5, pp.173-181, 1992. ,
Type-2 Computability and Moore's Recursive Functions, 6th Workshop on Computability and Complexity in Analysis Electronic Notes in Theoretical Computer Science, pp.83-95, 2004. ,
DOI : 10.1016/j.entcs.2004.06.036
Closed-form analytic maps in one and two dimensions can simulate universal turing machines, Theoretical Computer Science, vol.210, issue.1, pp.217-223, 1999. ,
DOI : 10.1016/S0304-3975(98)00117-0
MarieArnaudì es ? Cours de mathématiques , tome 2 : analyse, Dunod, LR87] Leonard Lipshitz et Lee A. Rubel ? « A differentially algebraic replacement theorem, and analog computability Proceedings of the American Mathematical Society 99, pp.367-372, 1974. ,
Finite and infinite machines [Moo96] Cristopher Moore ? « Recursion theory on the reals and continuous-time computation, Theoretical Computer Science, vol.162, issue.1, pp.23-44, 1967. ,
Müller ? « Subpolynomial complexity classes of real functions and real numbers, International Colloquium on Automata, Languages and Programming (ICALP 86) (L. Kott, pp.284-293, 1986. ,
A recursive function, defined on a compact interval and having a continuous derivative that is not recursive., The Michigan Mathematical Journal, vol.18, issue.2, pp.97-98, 1971. ,
DOI : 10.1307/mmj/1029000631
Pour-El ? « Abstract computability and its relations to the general purpose analog computer », Transactions of the, pp.1-28, 1974. ,
Pour-El et J. Ian Richards ? Computability in analysis and physics, 1989. ,
Rose ? Subrecursion : Functions and hierarchies, 1984. ,
Mathematical Theory of the Differential Analyzer, Journal of Mathematics and Physics, vol.XXII, issue.1-4, pp.337-354, 1941. ,
DOI : 10.2307/3607893
Siegelmann ? Neural networks and analog computation : Beyond the turing limit, 1999. ,
Church's thesis meets the N-body problem, Applied Mathematics and Computation, vol.178, issue.1, pp.154-183, 2006. ,
Sontag ? « Analog computation via neural networks », Theoretical Computer Science, vol.131, issue.2, pp.331-360, 1994. ,
Lord Kelvin) ? « On an instrument for calculating the integral of the product of two given functions, Proceedings of the Royal Society of London, pp.1876-266 ,
Beyond the First Main Theorem ??? When Is the Solution of a Linear Cauchy Problem Computable?, Lecture Notes in Computer Science, vol.3959, pp.783-792, 2006. ,
DOI : 10.1007/11750321_75