Computational Complexity of Space-Bounded Real Numbers

Masaki Nakanishi; Marcos Villagra

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arXiv · 1805.02572

Computational Complexity of Space-Bounded Real Numbers

Masaki Nakanishi·Marcos Villagra

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Abstract

In this work we study the space complexity of computable real numbers represented by fast convergent Cauchy sequences. We show the existence of families of trascendental numbers which are logspace computable, as opposed to algebraic irrational numbers which seem to required linear space. We characterized the complexity of space-bounded real numbers by quantifying the space complexities of tally sets. The latter result introduces a technique to prove the space complexity of real numbers by studying its corresponding tally sets, which is arguably a more natural approach. Results of this work present a new approach to study real numbers whose transcendence is unknown.

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Masaki Nakanishi, Marcos Villagra. 2018-05-07. Computational Complexity of Space-Bounded Real Numbers. https://arxiv.org/abs/1805.02572

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