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Closed-form analytic maps in one and two dimensions can simulate universal Turing machines
Theoretical Computer Science - Special issue on real numbers and computers
Achilles and the tortoise climbing up the arithmetical hierarchy
Journal of Computer and System Sciences - Fourteenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
Neural networks and analog computation: beyond the Turing limit
Neural networks and analog computation: beyond the Turing limit
Computable analysis: an introduction
Computable analysis: an introduction
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CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
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Theoretical Computer Science
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SIAM Journal on Control and Optimization
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CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
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This paper analyzes the computational power of dynamical systems robust to infinitesimal perturbations. Previous work on the subject has delved on very specific types of systems. Here we obtain results for broader classes of dynamical systems (including those systems defined by Lipschitz/analytic functions). In particular we show that systems robust to infinitesimal perturbations only recognize recursive languages. We also show the converse direction: every recursive language can be robustly recognized by a computable system. By other words we show that robustness is equivalent to decidability.