Complexity theory of real functions
Complexity theory of real functions
Universal computation and other capabilities of hybrid and continuous dynamical systems
Theoretical Computer Science - Special issue on hybrid systems
Recursion theory on the reals and continuous-time computation
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
Complexity and information
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Ordinary Differential Equations
Ordinary Differential Equations
An analog characterization of the Grzegorczyk hierarchy
Journal of Complexity
Real recursive functions and their hierarchy
Journal of Complexity
Type-2 Computability and Moore's Recursive Functions
Electronic Notes in Theoretical Computer Science (ENTCS)
Problems and prospects for quantum computational speed-up
ICCS'03 Proceedings of the 2003 international conference on Computational science
A survey of recursive analysis and Moore's notion of real computation
Natural Computing: an international journal
Robust simulations of turing machines with analytic maps and flows
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Real Recursive Functions and Baire Classes
Fundamenta Informaticae
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We explore recursion theory on the reals, the analog counterpart of recursive function theory. In recursion theory on the reals, the discrete operations of standard recursion theory are replaced by operations on continuous functions, such as composition and various forms of differential equations. We define classes of real recursive functions, in a manner similar to the classical approach in recursion theory, and we study their complexity. In particular, we prove both upper and lower bounds for several classes of real recursive functions, which lie inside the primitive recursive functions and, therefore, can be characterized in terms of standard computational complexity.