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
Computable analysis: an introduction
Computable analysis: an introduction
Iteration, inequalities, and differentiability in analog computers
Journal of Complexity
An analog characterization of the Grzegorczyk hierarchy
Journal of Complexity
µ-recursion and infinite limits
Theoretical Computer Science
Analog computers and recursive functions over the reals
Journal of Complexity
Real recursive functions and their hierarchy
Journal of Complexity
Elementarily computable functions over the real numbers and R-sub-recursive functions
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
The P ≠ NP conjecture in the context of real and complex analysis
Journal of Complexity
Recursive Analysis Characterized as a Class of Real Recursive Functions
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
Characterizing Computable Analysis with Differential Equations
Electronic Notes in Theoretical Computer Science (ENTCS)
A characterization of computable analysis on unbounded domains using differential equations
Information and Computation
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We use our method of approximation to relate various classes of computable functions over the reals. In particular, we compare Computable Analysis to the two analog models, the General Purpose Analog Computer and Real Recursive Functions. There are a number of existing results in the literature showing that the different models correspond exactly. We show how these exact correspondences can be broken down into a two step process of approximation and completion. We show that the method of approximation has further application in relating classes of functions, exploiting the transitive nature of the approximation relation. This work builds on our earlier work with our method of approximation, giving more evidence of the breadth of its applicability.