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2003•BRICS Report SeriesOpen access

A Two-Layer Approach to the Computability and Complexity of Real Numbers

Branimir Lambov

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Abstract

We present a new approach to computability of real numbers in which real functions have type-1 representations, which also includes the ability to reason about the complexity of real numbers and functions. We discuss how this allows efficient implementations of exact real numbers and also present a new real number system that is based on it.

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What this paper is about

We present a new approach to computability of real numbers in which real functions have type-1 representations, which also includes the ability to reason about the complexity of real numbers and functions. We discuss how this allows efficient implementations of exact real numbers and also present a new real number system that is based on it.

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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We present a new approach to computability of real numbers in which real functions have type-1 representations, which also includes the ability to reason about the complexity of real numbers and functions. We discuss how this allows efficient implementations of exact real numbers and also present a new real number system that is based on it.

Key concepts: Computability, Real number, Computer science, Mathematics, Discrete mathematics, Theoretical computer science, Arithmetic

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