Complexity theory of real functions
Complexity theory of real functions
A new recursion-theoretic characterization of the polytime functions
Computational Complexity
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
Complexity and information
Neural networks and analog computation: beyond the Turing limit
Neural networks and analog computation: beyond the Turing limit
Iteration, inequalities, and differentiability in analog computers
Journal of Complexity
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
The P ≠ NP conjecture in the context of real and complex analysis
Journal of Complexity
A new conceptual framework for analog computation
Theoretical Computer Science
The P≠NP conjecture in the context of real and complex analysis
Journal of Complexity
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Recursion theory on the reals, the analog counterpart of recursive function theory, is an approach to continuous-time computation inspired by the models of Classical Physics. 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 like indefinite integrals, linear differential equations and more general Cauchy problems. We define classes of real recursive functions in a manner similar to the standard recursion theory and we study their complexity. We prove both upper and lower bounds for several classes of real recursive functions, which lie inside the elementary functions, and can be characterized in terms of space complexity. In particular, we show that hierarchies of real recursive classes closed under restricted integration operations are related to the exponential space hierarchy. The results in this paper, combined with earlier results, suggest that there is a close connection between analog complexity classes and subrecursive classes, at least in the region between FLINSPACE and the primitive recursive functions.