Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Integer and combinatorial optimization
Integer and combinatorial optimization
Analog VLSI and neural systems
Analog VLSI and neural systems
Terminal attractors in neural networks
Neural Networks
Linear programming and network flows (2nd ed.)
Linear programming and network flows (2nd ed.)
Introduction to the theory of neural computation
Introduction to the theory of neural computation
Real functions, contraction mappings, and P-completeness
Information and Computation
Analog computation via neural networks
Theoretical Computer Science
Computability with low-dimensional dynamical systems
Theoretical Computer Science
Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
Computational Complexity of Two-Dimensional Regions
SIAM Journal on Computing
Recursion theory on the reals and continuous-time computation
Theoretical Computer Science - Special issue on real numbers and computers
Primal-dual interior-point methods
Primal-dual interior-point methods
Complexity and real computation
Complexity and real computation
Achilles and the Tortoise climbing up the hyper-arithmetical hierarchy
Theoretical Computer Science - Special issue on real numbers and computers
Closed-form analytic maps in one and two dimensions can simulate universal Turing machines
Theoretical Computer Science - Special issue on real numbers and computers
Analog computation with dynamical systems
PhysComp96 Proceedings of the fourth workshop on Physics and computation
Iteration, inequalities, and differentiability in analog computers
Journal of Complexity
Vision Chips: Implementing Vision Algorithms with Analog VLSI Circuits
Vision Chips: Implementing Vision Algorithms with Analog VLSI Circuits
Neural Networks for Optimization and Signal Processing
Neural Networks for Optimization and Signal Processing
Winner-Take-All Networks with Lateral Excitation
Analog Integrated Circuits and Signal Processing
IEEE Transactions on Neural Networks
Continuous-time symmetric Hopfield nets are computationally universal
Neural Computation
Probabilistic analysis of a differential equation for linear programming
Journal of Complexity
Exponential transients in continuous-time Liapunov systems
Theoretical Computer Science
Fast SVM Training Algorithm with Decomposition on Very Large Data Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Decidability and Universality in Symbolic Dynamical Systems
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
A new conceptual framework for analog computation
Theoretical Computer Science
Computational complexity of dynamical systems: The case of cellular automata
Information and Computation
The computational power of continuous dynamic systems
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
Decidability and Universality in Symbolic Dynamical Systems
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
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We present a model of computation with ordinary differential equations (ODEs) which converge to attractors that are interpreted as the output of a computation. We introduce a measure of complexity for exponentially convergent ODEs, enabling an algorithmic analysis of continuous time flows and their comparison with discrete algorithms. We define polynomial and logarithmic continuous time complexity classes and show that an ODE which solves the maximum network flow problem has polynomial time complexity. We also analyze a simple flow that solves the Maximum problem in logarithmic time. We conjecture that a subclass of the continuous P is equivalent to the classical P.