S. Aaronson, Guest Column: NP-complete problems and physical reality, ACM SIGACT News, vol.36, issue.1, pp.30-52, 2005.
DOI : 10.1145/1052796.1052804

H. Abdi, A NEURAL NETWORK PRIMER, Journal of Biological Systems, vol.02, issue.03, pp.247-281, 1994.
DOI : 10.1142/S0218339094000179

L. M. Adleman, Molecular computation of solutions to combinatorial problems, Science, vol.266, issue.5187, pp.1021-1024, 1994.
DOI : 10.1126/science.7973651

. Alur, The algorithmic analysis of hybrid systems, Theoretical Computer Science, vol.138, issue.1, pp.3-34, 1995.
DOI : 10.1016/0304-3975(94)00202-T

D. Alur, R. Alur, and D. L. Dill, Automata for modeling realtime systems, Automata, Languages and Programming, 17th International Colloquium Proceedings, volume 443 of Lecture Notes in Computer Science, pp.322-335, 1990.

D. Alur, R. Alur, and D. L. Dill, A theory of timed automata, Theoretical Computer Science, vol.126, issue.2, pp.183-235, 1994.
DOI : 10.1016/0304-3975(94)90010-8

M. Alur, R. Alur, and P. Madhusudan, Decision Problems for Timed Automata: A Survey, Lecture Notes in Computer Science, vol.3185, pp.1-24, 2004.
DOI : 10.1007/978-3-540-30080-9_1

V. I. Arnold and . Johnson, Mathematical methods of classical mechanics, volume 60 of Graduate texts in Mathematics Mechanisms for the generation of plane curves, 1964.

E. Asarin, Chaos and undecidabilty (draft) Avalaible in http, 1995.

E. E. Asarin, E. Asarin, and A. Bouajjani, Equations on timed languages Noise and decidability. Continuous Dynamics and Computability Colloquium. Video and sound available trough " Diffusion des savoirs de l'Ecole Normale Supérieure Perturbed Turing machines and hybrid systems, Hybrid Systems: Computation and Control, First International Workshop, HSCC'98 Proceedings, volume 1386 of Lecture Notes in Computer Science Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science, pp.1-12, 1998.

. Asarin, A Kleene theorem for timed automata, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science, pp.160-171, 1997.
DOI : 10.1109/LICS.1997.614944

. Asarin, Timed regular expressions, Journal of the ACM, vol.49, issue.2, pp.172-206, 2002.
DOI : 10.1145/506147.506151

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

C. Asarin, E. Asarin, P. L. Collins, G. F. Italiano, L. Monteiro et al., Noisy Turing Machines, Caires, Automata , Languages and Programming, 32nd International Colloquium, ICALP 2005 Proceedings, pp.1031-1042, 2005.
DOI : 10.1007/11523468_83

URL : https://hal.archives-ouvertes.fr/hal-00157585

D. Asarin, E. Asarin, and C. Dima, Balanced timed regular expressions, Electronic Notes in Theoretical Computer Science, issue.5, p.68, 2002.
DOI : 10.1145/506147.506151

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

M. Asarin, E. Asarin, and O. Maler, Achilles and the Tortoise Climbing Up the Arithmetical Hierarchy, Journal of Computer and System Sciences, vol.57, issue.3, pp.389-398, 1998.
DOI : 10.1006/jcss.1998.1601

. Asarin, Reachability analysis of dynamical systems having piecewise-constant derivatives, Theoretical Computer Science, vol.138, issue.1, pp.35-65, 1995.
DOI : 10.1016/0304-3975(94)00228-B

E. Asarin and G. Schneider, Widening the Boundary between Decidable and Undecidable Hybrid Systems*, CONCUR 2002 -Concurrency Theory, 13th International Conference Proceedings, volume 2421 of Lecture Notes in Computer Science, pp.193-208, 2002.
DOI : 10.1007/3-540-45694-5_14

. Asarin, On the Decidability of the Reachability Problem for Planar Differential Inclusions, Hybrid Systems: Computation and Control Proceedings Foundations of Software Science and Computation Structure, First International Conference, FoSSaCS'98, Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS'98 Proceedings, volume 1378 of Lecture Notes in Computer Science, pp.89-104, 1998.
DOI : 10.1007/3-540-45351-2_11

. Ben-hur, Probabilistic analysis of a differential equation for linear programming, Journal of Complexity, vol.19, issue.4, pp.474-510, 2003.
DOI : 10.1016/S0885-064X(03)00032-3

. Ben-hur, Random matrix theory for the analysis of the performance of an analog computer: a scaling theory, Physics Letters A, vol.323, issue.3-4, pp.3-4204, 2004.
DOI : 10.1016/j.physleta.2004.01.069

. Ben-hur, On probabilistic analog automata, Theoretical Computer Science, vol.320, issue.2-3, pp.2-3449, 2004.
DOI : 10.1016/j.tcs.2004.03.003

URL : http://doi.org/10.1016/j.tcs.2004.03.003

. Ben-hur, A Theory of Complexity for Continuous Time Systems, Journal of Complexity, vol.18, issue.1, pp.51-86, 2002.
DOI : 10.1006/jcom.2001.0581

T. Blondel, V. D. Blondel, and J. N. Tsitsiklis, Complexity of stability and controllability of elementary hybrid systems, Automatica, vol.35, issue.3, pp.479-489, 1999.
DOI : 10.1016/S0005-1098(98)00175-7

V. D. Blondel and J. N. Tsitsiklis, A survey of computational complexity results in systems and control, Automatica, vol.36, issue.9, pp.1249-1274, 2000.
DOI : 10.1016/S0005-1098(00)00050-9

. Blum, Complexity and Real Computation, 1998.
DOI : 10.1007/978-1-4612-0701-6

. Blum, 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

. Bournez and O. Bournez, Achilles and the Tortoise climbing up the hyper-arithmetical hierarchy, Theoretical Computer Science, vol.210, issue.1, pp.21-71, 1999.
DOI : 10.1016/S0304-3975(98)00096-6

O. Bournez and O. Bournez, How much can analog and hybrid systems be proved (super-)Turing, Applied Mathematics and Computation, vol.178, issue.1, pp.58-71, 1999.
DOI : 10.1016/j.amc.2005.09.070

URL : https://hal.archives-ouvertes.fr/inria-00000517

. Bournez, Polynomial differential equations compute all real computable functions on computable compact intervals, Journal of Complexity, vol.23, issue.3, 2007.
DOI : 10.1016/j.jco.2006.12.005

URL : https://hal.archives-ouvertes.fr/inria-00102947

. Bournez, . Hainry, O. Bournez, and E. Hainry, Elementarily computable functions over the real numbers and R-sub-recursive functions, Theoretical Computer Science, vol.348, pp.2-3130, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00107812

. Bournez, . Hainry, O. Bournez, and E. Hainry, Recursive analysis characterized as a class of real recursive functions, Fundamenta Informaticae, vol.74, issue.4, pp.409-433, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00000515

. Bouyer, Are timed automata updatable, Computer Aided Verification, 12th International Conference Proceedings, volume 1855 of Lecture Notes in Computer Science, pp.464-479, 2000.
DOI : 10.1007/10722167_35

URL : https://hal.archives-ouvertes.fr/hal-00350488

. Bouyer, Expressiveness of Updatable Timed Automata, Mathematical Foundations of Computer Science 25th International Symposium, MFCS 2000 Proceedings, volume 1893 of Lecture Notes in Computer Science, pp.232-242, 2000.
DOI : 10.1007/3-540-44612-5_19

URL : https://hal.archives-ouvertes.fr/hal-00350490

. Bouyer, . Petit, P. Bouyer, and A. Petit, Decomposition and Composition of Timed Automata, Automata, Languages and Programming, 26th International Colloquium, ICALP'99 Proceedings, volume 1644 of Lecture Notes in Computer Science, pp.210-219, 1999.
DOI : 10.1007/3-540-48523-6_18

. Bouyer, . Petit, P. Bouyer, and A. Petit, A Kleene/Büchi-like theorem for clock languages, Journal of Automata, Languages and Combinatorics, vol.7, issue.2, pp.167-186, 2002.

M. D. Bowles, U.S. technological enthusiasm and British technological skepticism in the age of the analog brain, IEEE Annals of the History of Computing, vol.18, issue.4, pp.5-15, 1996.
DOI : 10.1109/85.539911

. Branicky, M. S. Branicky, and M. S. Branicky, Universal computation and other capabilities of hybrid and continuous dynamical systems, Theoretical Computer Science, vol.138, issue.1, pp.67-100, 1995.
DOI : 10.1016/0304-3975(94)00147-B

T. Brihaye, A note on the undecidability of the reachability problem for o-minimal dynamical systems, MLQ, vol.309, issue.2, pp.165-170, 2006.
DOI : 10.1002/malq.200510024

. Brihaye, T. Michaux-]-brihaye, and C. Michaux, On the expressiveness and decidability of o-minimal hybrid systems, Journal of Complexity, vol.21, issue.4, pp.447-478, 2005.
DOI : 10.1016/j.jco.2004.09.003

R. W. Brockett and R. W. Brockett, Smooth dynamical systems which realize arithmetical and logical operations Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems, Three Decades of Mathematical Systems Theory, pp.19-3079, 1989.

R. W. Brockett, R. M. Helmke, J. Saurer, and V. Bush, Dynamical systems and their associated automata The differential analyser, Systems and Networks: Mathematical Theory and Applications, pp.49-69447, 1931.

. Calude, C. S. Pavlov-]-calude, and B. Pavlov, Coins, quantum measurements , and Turing's barrier, Quantum Information Processing, vol.1, issue.1/2, pp.107-127, 2002.
DOI : 10.1023/A:1019623616675

. Campagnolo, Iteration, Inequalities, and Differentiability in Analog Computers, Journal of Complexity, vol.16, issue.4, pp.642-660, 2000.
DOI : 10.1006/jcom.2000.0559

. Campagnolo, An Analog Characterization of the Grzegorczyk Hierarchy, Journal of Complexity, vol.18, issue.4, pp.977-1000, 2002.
DOI : 10.1006/jcom.2002.0655

M. L. Campagnolo and M. L. Campagnolo, Computational complexity of real valued recursive functions and analog circuits The complexity of real recursive functions Continuous time computation with restricted integration capabilities, Unconventional Models of Computation, UMC'02, number 2509 in Lecture Notes in Computer Science, pp.1-14147, 2001.

M. L. Ojakian and K. , The elementary computable functions over the real numbers: applying two new techniques. Archives for Mathematical Logic, 2007.

M. Casey, The Dynamics of Discrete-Time Computation, with Application to Recurrent Neural Networks and Finite State Machine Extraction, Neural Computation, vol.2, issue.4, pp.1135-1178, 1996.
DOI : 10.1146/annurev.ph.47.030185.000333

M. Casey, Correction to Proof That Recurrent Neural Networks Can Robustly Recognize Only Regular Languages, Neural Computation, vol.10, issue.5, pp.1067-1069, 1998.
DOI : 10.1162/neco.1996.8.6.1135

V. Ceraens, K. Ceraens, and J. Viksna, Deciding reachability for planar multi-polynomial systems, Hybrid Systems III, p.389, 1996.
DOI : 10.1007/BFb0020962

A. Church, An Unsolvable Problem of Elementary Number Theory, American Journal of Mathematics, vol.58, issue.2, pp.345-363, 1936.
DOI : 10.2307/2371045

P. Clote, Computational models and function algebras, Handbook of Computability Theory, pp.589-681, 1998.

. Coddington, E. A. Levinson-]-coddington, and N. Levinson, Theory of Ordinary Differentiel Equations, 1972.

P. Collins, Continuity and computability of reachable sets, Theoretical Computer Science, vol.341, issue.1-3, pp.162-195, 2005.
DOI : 10.1016/j.tcs.2005.05.001

C. , L. Collins, P. Lygeros, and J. , Computability of finitetime reachable sets for hybrid systems, Proceedings of the 44th IEEE Conference on Decision and Control and the European Control Conference, pp.4688-4693, 2005.

P. Collins and J. H. Van-schuppen, Observability of Piecewise-Affine Hybrid Systems, Hybrid Systems: Computation and Control, 7th International Workshop Proceedings, volume 2993 of Lecture Notes in Computer Science, pp.265-279, 2004.
DOI : 10.1007/978-3-540-24743-2_18

B. J. Copeland, Even Turing machines can compute uncomputable functions, Unconventional Models of Computations, 1998.

B. J. Copeland, Accelerating Turing machines. Minds and Machines, pp.281-301, 2002.

C. , M. Costa, J. F. Mycka, J. Bekmann, A. Berger et al., The conjecture P = N P given by some analytic condition Doug Coward's Analog Computer Museum, Logical Approaches to Computational Barriers, Second conference on Computability in Europe, pp.47-57, 2006.

E. B. Davies, Building Infinite Machines, The British Journal for the Philosophy of Science, vol.52, issue.4, pp.671-682, 2001.
DOI : 10.1093/bjps/52.4.671

. Dee, D. Dee, and M. Ghil, Boolean Difference Equations, I: Formulation and Dynamic Behavior, SIAM Journal on Applied Mathematics, vol.44, issue.1, pp.111-126, 1984.
DOI : 10.1137/0144009

. Delvenne, Computational Universality in Symbolic Dynamical Systems, MCU: International Conference on Machines, Computations, and Universality, pp.104-115, 2004.
DOI : 10.1007/978-3-540-31834-7_8

D. Deutsch, Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer, Series A, pp.97-117, 1985.
DOI : 10.1098/rspa.1985.0070

J. Durand-lose, Abstract Geometrical Computation: Turing-Computing Ability and Undecidability, New Computational Paradigms, First Conference on Computability in Europe Proceedings, volume 3526 of Lecture Notes in Computer Science, pp.106-116, 2005.
DOI : 10.1007/11494645_14

URL : https://hal.archives-ouvertes.fr/hal-00079815

N. Earman, J. Earman, and J. D. Norton, Forever Is a Day: Supertasks in Pitowsky and Malament-Hogarth Spacetimes, Philosophy of Science, vol.60, issue.1, pp.22-42, 1993.
DOI : 10.1086/289716

. Etesi, . Németi, G. Etesi, and I. Németi, Non-Turing computations via Malament-Hogarth space-times, International Journal of Theoretical Physics, vol.41, issue.2, pp.341-370, 2002.
DOI : 10.1023/A:1014019225365

L. Faybusovich, Dynamical Systems which Solve Optimization Problems with Linear Constraints, IMA Journal of Mathematical Control and Information, vol.8, issue.2, pp.135-149, 1991.
DOI : 10.1093/imamci/8.2.135

L. Faybusovich, Hamiltonian structure of dynamical systems which solve linear programming problems, Physica D: Nonlinear Phenomena, vol.53, issue.2-4, pp.217-232, 1991.
DOI : 10.1016/0167-2789(91)90062-E

A. Filippov, Differential equations with discontinuous righthand sides, 1988.
DOI : 10.1007/978-94-015-7793-9

O. Finkel, On the shuffle of regular timed languages, Bulletin of the European Association for Theoretical Computer Science, vol.88, pp.182-184, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00111151

J. Foy, A dynamical system which must be stable whose stability cannot be proved, Theoretical Computer Science, vol.328, issue.3, pp.355-361, 2004.
DOI : 10.1016/j.tcs.2004.05.001

A. P. Francisco and M. Fränzle, Finite automata over continuous time. Diploma Thesis Instituto Superior Técnico Analysis of hybrid systems: An ounce of realism can save an infinity of states, Computer Science Logic (CSL'99), volume 1683 of Lecture Notes in Computer Science, pp.126-140, 1999.

. Gori, . Meer, M. Gori, and K. Meer, A Step towards a Complexity Theory for Analog Systems, MLQ, vol.48, issue.S1, pp.4845-58, 2002.
DOI : 10.1002/1521-3870(200210)48:1+<45::AID-MALQ45>3.0.CO;2-7

. Graça, Robust Simulations of Turing Machines with Analytic Maps and Flows, Proceedings of CiE'05, New Computational Paradigms, pp.169-179, 2005.
DOI : 10.1007/11494645_21

. Graça, Computability with polynomial differential equations, Advances in Applied Mathematics, 2007.

. Graça, Computability, noncomputability and undecidability of maximal intervals of IVPs. Transactions of the, 2006.

D. Graça, The general purpose analog computer and recursive functions over the reals, 2002.

D. S. Graça, Some recent developments on Shannon's general purpose analog computer, Mathematical Logic Quarterly, vol.50, pp.4-5473, 2004.

D. S. Graça and J. F. Costa, Analog computers and recursive functions over the reals, Journal of Complexity, vol.19, issue.5, pp.644-664, 2003.
DOI : 10.1016/S0885-064X(03)00034-7

M. Grigorieff, S. Grigorieff, and M. Margenstern, Register cellular automata in the hyperbolic plane, Fundamenta Informaticae, vol.1, issue.61, pp.19-27, 2004.

J. Gruska, Foundations of Computing, 1997.

. Gupta, Robust timed automata Hybrid and Real-Time Systems, International Workshop Formal language theory and DNA: An analysis of the generative capacity of specific recombinant behaviors, Proceedings, volume 1201 of Lecture Notes in Computer Science, pp.331-345737, 1987.

M. Helmke, U. Helmke, J. Moore, and . Henzinger, Optimization and Dynamical Systems Communications and Control Engineering Series What's decidable about hybrid automata, Journal of Computer and System Sciences, vol.57, issue.1, pp.94-124, 1994.

T. A. Henzinger and J. Raskin, Robust Undecidability of Timed and Hybrid Systems, Hybrid Systems: Computation and Control, Third International Workshop Proceedings, volume 1790 of Lecture Notes in Computer Science, pp.145-159, 2000.
DOI : 10.1007/3-540-46430-1_15

. Hirsch, Differential Equations, Dynamical Systems, and an Introduction to Chaos Non-Turing computers and non-Turing computability, Proceedings of the Philosophy of Science Association (PSA'94), pp.126-138, 1994.

M. Hogarth, Predictability, Computability and Spacetime, 1996.

M. L. Hogarth, Available for download on www Does general relativity allow an observer to view an eternity in a finite time? Foundations of Physics Letters, hypercomputation.net, vol.5, pp.173-181, 1992.

J. J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons., Proceedings of the National Academy of Sciences, vol.81, issue.10, pp.3088-3092, 1984.
DOI : 10.1073/pnas.81.10.3088

T. Hopfield, J. J. Hopfield, and D. W. Tank, Neural' computation of decisions in optimization problems, Biological Cybernetics, vol.52, pp.141-152, 1985.

E. Paris, Dynamical systems: stability and simulability, 2006.

A. Kempe, On a general method of describing plane curves of the n?th degree by linkwork, Proceedings of the, pp.213-216, 1876.

T. D. Kieu, Hypercomputation with quantum adiabatic processes, Theoretical Computer Science, vol.317, issue.1-3, pp.93-104, 2004.
DOI : 10.1016/j.tcs.2003.12.006

S. C. Kleene, General recursive functions of natural numbers, Mathematische Annalen, vol.110, issue.1, pp.727-742, 1936.
DOI : 10.1007/BF01565439

K. Ko, On the computational complexity of ordinary differential equations, Information and Control, vol.58, issue.1-3, pp.1-3157, 1983.
DOI : 10.1016/S0019-9958(83)80062-X

K. Ko and P. Koiran, Complexity Theory of Real Functions Progress in Theoretical Computer Science The topological entropy of iterated piecewise affine maps is uncomputable, Birkhäuser, Boston. Discrete Mathematics & Theoretical Computer Science, vol.4, issue.2, pp.351-356, 1991.

. Koiran, Computability with low-dimensional dynamical systems, Theoretical Computer Science, vol.132, issue.1-2, pp.113-128, 1994.
DOI : 10.1016/0304-3975(94)90229-1

. Koiran, P. Moore-]-koiran, and C. Moore, 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

V. Korovina and N. Vorobjov, Pfaffian Hybrid Systems, Computer Science Logic, 18th International Workshop 13th Annual Conference of the EACSL Proceedings, volume 3210 of Lecture Notes in Computer Science, pp.430-441, 2004.
DOI : 10.1007/978-3-540-30124-0_33

. Korovina, . Vorobjov, M. V. Korovina, and N. Vorobjov, Upper and Lower Bounds on Sizes of Finite Bisimulations of Pfaffian Hybrid Systems, Logical Approaches to Computational Barriers, Second Conference on Computability in Europe Proceedings, pp.267-276, 2006.
DOI : 10.1016/S0022-4049(99)00017-1

. Kurganskyy, . Potapov, O. Kurganskyy, I. C. Potapov, M. J. Dinneen et al., Computation in One-Dimensional Piecewise Maps and Planar Pseudo-Billiard Systems, Unconventional Computation, 4th International Conference Proceedings, pp.169-175, 2005.
DOI : 10.1007/11560319_16

. Lafferriere, G. Pappas-]-lafferriere, and G. J. Pappas, O-Minimal Hybrid Systems, Mathematics of Control, Signals, and Systems, vol.13, issue.1, pp.1-21, 2000.
DOI : 10.1007/PL00009858

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

M. Legenstein, R. Legenstein, and W. Maass, What makes a dynamical system computationally powerful?, New Directions in Statistical Signal Processing: From Systems to Brain, pp.127-154, 2007.

. Lipshitz, L. Lipshitz, and L. A. Rubel, A differentially algebraic replacement theorem, and analog computability, Proceedings of the, pp.367-372, 1987.

R. J. Lipton, DNA solution of hard computational problems, Science, vol.268, issue.5210, pp.542-545, 1995.
DOI : 10.1126/science.7725098

B. Loff and . Loff, A functional characterisation of the analytical hierarchy Computation and Logic in the Real World Computability on reals , infinite limits and differential equations, Computability in Europe, 2007.

. Loff, The new promise of analog computation, Computability in Europe 2007: Computation and Logic in the Real World, 2007.

W. Maass, Lower Bounds for the Computational Power of Networks of Spiking Neurons, Neural Computation, vol.202, issue.1, pp.1-40, 1996.
DOI : 10.1090/S0002-9947-1985-0808746-4

W. Maass, On the computational power of noisy spiking neurons, Advances in Neural Information Processing Systems, pp.211-217, 1996.

W. Maass, A Model for Fast Analog Computations with Noisy Spiking Neurons, Computational Neuroscience: Trends in research, pp.123-127, 1997.
DOI : 10.1007/978-1-4757-9800-5_20

W. Maass, Networks of spiking neurons: The third generation of neural network models, Neural Networks, vol.10, issue.9, pp.1659-1671, 1997.
DOI : 10.1016/S0893-6080(97)00011-7

W. Maass, Computing with spiking neurons, Pulsed Neural Networks, pp.55-85, 1999.

W. Maass, Computing with spikes. Special Issue on Foundations of Information Processing of TELEMATIK, pp.32-36, 2002.

. Maass, Computational aspects of feedback in neural circuits, Public Library of Science Computational Biology, vol.3, issue.1, pp.1-20, 2007.

W. Maass and T. Natschläger, A Model for Fast Analog Computation Based on Unreliable Synapses, Neural Computation, vol.78, issue.6, pp.1679-1704, 2000.
DOI : 10.1016/S0006-3495(72)86068-5

O. Maass, W. Maass, and P. Orponen, On the Effect of Analog Noise in Discrete-Time Analog Computations, Neural Computation, vol.18, issue.5, pp.1071-1095, 1998.
DOI : 10.1137/1116025

R. Maass, W. Maass, and B. Ruf, On computation with pulses. Information and Computation, pp.202-218, 1999.

S. Maass, W. Maass, and E. Sontag, Analog Neural Nets with Gaussian or Other Common Noise Distributions Cannot Recognize Arbitrary Regular Languages, Neural Computation, vol.39, issue.1, pp.771-782, 1999.
DOI : 10.1016/S0019-9958(63)90290-0

B. J. Maclennan, J. Mills, J. W. Mills, B. Himebaugh, A. Allred et al., Can differential equations compute? citeseer.ist.psu Programmable VLSI extended analog computer for cyclotron beam control Extended analog computers: A unifying paradigm for VLSI, plastic and colloidal computing systems Unpredictability and undecidability in dynamical systems, Workshop on Unique Chips and Systems (UCAS-1). Held in conjunction with IEEE International Symposium on Performance Analysis of Systems and Software (ISPASS05), pp.642354-2357, 1990.

C. Moore, Generalized shifts: unpredictability and undecidability in dynamical systems, Nonlinearity, vol.4, issue.2, pp.199-230, 1991.
DOI : 10.1088/0951-7715/4/2/002

C. Moore, Recursion theory on the reals and continuous-time computation, Theoretical Computer Science, vol.162, issue.1, pp.23-44, 1996.
DOI : 10.1016/0304-3975(95)00248-0

C. Moore, Dynamical recognizers: real-time language recognition by analog computers, Theoretical Computer Science, vol.201, issue.1-2, pp.99-136, 1998.
DOI : 10.1016/S0304-3975(97)00028-5

C. Moore, Finite-dimensional analog computers: Flows, maps, and recurrent neural networks, Unconventional Models of Computation (UMC'98, 1998.

J. D. Murray, Mathematical Biology. I: An Introduction, 2002.

C. Mycka, J. Mycka, and J. F. Costa, Real recursive functions and their hierarchy, Journal of Complexity, vol.20, issue.6, pp.835-857, 2004.
DOI : 10.1016/j.jco.2004.06.001

C. Mycka, J. Mycka, and J. F. Costa, What lies beyond the mountains? Computational systems beyond the Turing limit, European Association for Theoretical Computer Science Bulletin, vol.85, pp.181-189, 2005.

C. Mycka, J. Mycka, and J. F. Costa, The <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>P</mml:mi><mml:mo>???</mml:mo><mml:mtext><ce:italic>NP</ce:italic></mml:mtext></mml:math> conjecture in the context of real and complex analysis, Journal of Complexity, vol.22, issue.2, pp.287-303, 2006.
DOI : 10.1016/j.jco.2005.07.003

C. Mycka, J. Mycka, and J. F. Costa, A new conceptual framework for analog computation, Theoretical Computer Science, vol.374, issue.1-3, pp.277-290, 2007.
DOI : 10.1016/j.tcs.2007.01.005

M. Müller, N. Müller, and B. Moiske, Solving initial value problems in polynomial time, Proc. 22 JAIIO -PANEL '93, Part 2, pp.283-293, 1993.

W. Maass, Spiking neurons and the induction of finite state machines, Theoretical Computer Science: Special Issue on Natural Computing, vol.287, issue.1, pp.251-265, 2002.

. Németi, . Andréka, I. Németi, H. Andréka, J. Wiedermann et al., New Physics and Hypercomputation, SOFSEM 2006: Theory and Practice of Computer Science, 32nd Conference on Current Trends in Theory and Practice of Computer Science, Merín, Czech Republic Proceedings, p.63, 2006.
DOI : 10.1007/11611257_6

. Németi, . Dávid, I. Németi, and G. Dávid, Relativistic computers and the Turing barrier, Applied Mathematics and Computation, vol.178, issue.1, pp.118-142, 2006.
DOI : 10.1016/j.amc.2005.09.075

. Nicollin, An approach to the description and analysis of hybrid systems, Hybrid Systems, pp.149-178, 1993.
DOI : 10.1007/3-540-57318-6_28

S. Omohundro, Modelling cellular automata with partial differential equations, Physica D: Nonlinear Phenomena, vol.10, issue.1-2, pp.128-134, 1984.
DOI : 10.1016/0167-2789(84)90255-0

P. Orponen, Computational complexity of neural networks: a survey, Nordic Journal of Computing, vol.1, issue.1, pp.94-110, 1994.

P. Orponen, The Computational Power of Discrete Hopfield Nets with Hidden Units, Neural Computation, vol.20, issue.2, pp.403-415, 1996.
DOI : 10.1016/0304-3975(86)90091-5

P. Orponen, A Survey of Continuous-Time Computation Theory, Advances in Algorithms, Languages, and Complexity, pp.209-224, 1997.
DOI : 10.1007/978-1-4613-3394-4_11

P. Orponen and J. , A continuous-time Hopfield net simulation of discrete neural networks, Proceedings of the 2nd International ICSC Symposium on Neural Computations (NC'2000), pp.36-42, 2000.

C. Papadimitriou, Algorithms, games, and the Internet, Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, pp.749-753, 2001.

G. P?-aun and E. Post, Membrane Computing. An Introduction A variant of a recursively unsolvable problem, Bulletin of the American Math. Soc, vol.52, pp.264-268, 1946.

M. Zhong and N. , The wave equation with computable initial data whose unique solution is nowhere computable, Mathematical Logic Quarterly, vol.43, issue.4, pp.499-509, 1997.

M. B. Richards and J. I. , A computable ordinary differential equation which possesses no computable solution, Annals of Mathematical Logic, vol.17, pp.61-90, 1979.

M. B. Richards and J. I. , The wave equation with computable initial data such that its unique solution is not computable, Advances in Mathematics, vol.39, pp.215-239, 1981.

A. Puri, Dynamical properties of timed automata, Formal Techniques in Real-Time and Fault-Tolerant Systems , 5th International Symposium, FTRTFT'98 Proceedings, volume 1486 of Lecture Notes in Computer Science, pp.210-227, 1998.
DOI : 10.1007/BFb0055349

. Puri, . Varaiya, A. Puri, and P. Varaiya, Decidability of hybrid systems with rectangular differential inclusions, Computer Aided Verification, 6th International Conference, CAV '94 Proceedings, pp.95-104, 1994.
DOI : 10.1007/3-540-58179-0_46

M. O. Rabin, Probabilistic automata, Information and Control, vol.6, issue.3, pp.230-245, 1963.
DOI : 10.1016/S0019-9958(63)90290-0

A. Rabinovich, Automata over continuous time, Theoretical Computer Science, vol.300, issue.1-3, pp.1-3331, 2003.
DOI : 10.1016/S0304-3975(02)00331-6

. Rabinovich, . Trakhtenbrot, A. M. Rabinovich, and B. A. Trakhtenbrot, From finite automata toward hybrid systems (Extended abstract), Fundamentals of Computation Theory, 11th International Symposium, FCT '97 Proceedings, volume 1279 of Lecture Notes in Computer Science, pp.411-422, 1997.
DOI : 10.1007/BFb0036202

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

L. A. Rubel, A Survey of Transcendentally Transcendental Functions, The American Mathematical Monthly, vol.96, issue.9, pp.777-788, 1989.
DOI : 10.2307/2324840

L. A. Rubel, The Extended Analog Computer, Advances in Applied Mathematics, vol.14, issue.1, pp.39-50, 1993.
DOI : 10.1006/aama.1993.1003

K. Ruohonen, Undecidability of event detection for ODEs, Journal of Information Processing and Cybernetics, vol.29, pp.101-113, 1993.

K. Ruohonen and K. Ruohonen, Event detection for ODES and nonrecursive hierarchies, Proceedings of the Colloquium in Honor of Arto Salomaa, pp.358-371151, 1994.
DOI : 10.1007/3-540-58131-6_59

K. Ruohonen, Decidability and complexity of event detection problems for ODEs, Complexity, vol.2, issue.6, pp.41-53, 1997.
DOI : 10.1002/(SICI)1099-0526(199707/08)2:6<41::AID-CPLX9>3.0.CO;2-K

K. Ruohonen, Undecidable event detection problems for ODEs of dimension one and two, Theoretical Informatics and Applications, pp.67-79, 1997.
DOI : 10.1051/ita/1997310100671

K. Ruohonen, Chomskian Hierarchies of Families of Sets of Piecewise Continuous Functions, Theory of Computing Systems, pp.609-638, 2004.
DOI : 10.1007/s00224-004-1176-0

C. E. Shannon, Mathematical Theory of the Differential Analyzer, Journal of Mathematics and Physics, vol.XXII, issue.1-4, pp.337-354, 1941.
DOI : 10.1002/sapm1941201337

P. W. Shor, Algorithms for quantum computation: discrete logarithms and factoring, Proceedings 35th Annual Symposium on Foundations of Computer Science, pp.124-134, 1994.
DOI : 10.1109/SFCS.1994.365700

F. Siegelmann, H. T. Siegelmann, and S. Fishman, Analog computation with dynamical systems, Physica D: Nonlinear Phenomena, vol.120, issue.1-2, pp.214-235, 1998.
DOI : 10.1016/S0167-2789(98)00057-8

S. Siegelmann, H. T. Siegelmann, and E. D. Sontag, Analog computation via neural networks, Theoretical Computer Science, vol.131, issue.2, pp.331-360, 1994.
DOI : 10.1016/0304-3975(94)90178-3

URL : http://doi.org/10.1016/0304-3975(94)90178-3

S. Siegelmann, H. T. Siegelmann, and E. D. Sontag, On the computational power of neural nets, Proceedings of the fifth annual workshop on Computational learning theory , COLT '92, pp.132-150, 1995.
DOI : 10.1145/130385.130432

O. Síma, J. Síma, and P. Orponen, Exponential transients in continuous-time Liapunov systems, Síma and Orponen, pp.353-372693, 2003.
DOI : 10.1016/S0304-3975(03)00310-4

. Síma, . Orponen, J. Síma, and P. Orponen, General-purpose computation with neural networks: A survey of complexity theoretic results, Neural Computation, issue.12, pp.152727-2778, 2003.

W. D. Smith and W. D. Smith, Church???s thesis meets the N-body problem, Applied Mathematics and Computation, vol.178, issue.1, pp.154-183, 1998.
DOI : 10.1016/j.amc.2005.09.077

L. Stoll, H. M. Stoll, L. S. Lee, and A. Svoboda, A continuous-time optical neural network Computing Mechanisms and Linkages, IEEE Second International Conference on Neural Networks (2nd ICNN'88), volume II, pp.373-384, 1948.

W. Thomson, On an Instrument for Calculating Formula, the Integral of the Product of Two Given Functions, Proceedings of the Royal Society of London, pp.266-276, 1876.
DOI : 10.1098/rspl.1875.0034

B. Trakhtenbrot and B. A. Trakhtenbrot, Origins and metamorphoses of the trinity: Logic, nets, automata Automata and their interaction: Definitional suggestions, Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science Fundamentals of Computation Theory, 12th International Symposium, FCT '99 Proceedings, volume 1684 of Lecture Notes in Computer Science, pp.506-507, 1995.

Z. Tucker, J. V. Tucker, and J. I. Zucker, Computability of analog networks, Theoretical Computer Science, vol.371, issue.1-2, pp.115-146, 2007.
DOI : 10.1016/j.tcs.2006.10.018

A. Turing, On computable numbers, with an application to the Entscheidungsproblem¨, Entscheidungsproblem¨Entscheidungsproblem¨. Proceedings of the London Mathematical Society, vol.42, issue.2, pp.230-265, 1936.

. Vergis, The complexity of analog computation, Mathematics and Computers in Simulation, vol.28, issue.2, pp.91-113, 1986.
DOI : 10.1016/0378-4754(86)90105-9

K. Weihrauch, K. Weihrauch, and N. Zhong, Computable Analysis Is wave propagation computable or can wave computers beat the Turing machine?, Weihrauch and Zhong, pp.312-332, 2000.

P. D. Welch, The Extent of Computation in Malament-Hogarth Spacetimes, The British Journal for the Philosophy of Science, vol.59, issue.4, 2006.
DOI : 10.1093/bjps/axn031

M. R. Williams, About this issue, IEEE Annals of the History of Computing, vol.18, issue.4, 1996.

D. Naughton and T. J. , An optical model of computation, Theoretical Computer Science, vol.334, pp.1-3227, 2005.