
Set Turing Machines
We define a generalization of the Turing machine that computes on genera...
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SemiCountable Sets and their Application to Search Problems
We present the concept of the information efficiency of functions as a t...
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Continuous and monotone machines
We investigate a variant of the fuelbased approach to modeling divergin...
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Property and structure in constructive analysis
Real numbers such as Dedekind reals or (quotiented) Cauchy reals (as opp...
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Hilbert's Tenth Problem in Coq
We formalise the undecidability of solvability of Diophantine equations,...
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Computational Complexity of SpaceBounded Real Numbers
In this work we study the space complexity of computable real numbers re...
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Betwixt Turing and Kleene
Turing's famous 'machine' model constitutes the first intuitively convin...
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A recursion theoretic foundation of computation over real numbers
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by Gödel and Kleene. We show that this class of functions can also be characterized by masterslave machines, which are Turing machine like devices. The proof of the characterization gives a normal form theorem in the style of Kleene. Furthermore, this characterization is a natural combination of two most influential theories of computation over real numbers, namely, the typetwo theory of effectivity (TTE) (see, for example, Weihrauch) and the BlumShubSmale model of computation (BSS). Under this notion of computability, the recursive (or computable) subsets of real numbers are exactly effective Δ^0_2 sets.
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