### Theory and Applications of Models of Computation / Takayuki Kihara; Arno Pauly

Volume: 11436, Start page: 378

Swansea University Author:

• PDF | Accepted Manuscript

DOI (Published version): 10.1007/978-3-030-14812-6

Abstract

We study the Weihrauch degrees of closed choice for finite sets, closed choice for convex sets and sorting infinite sequences over finite alphabets. Our main result is that choice for finite sets of cardinality $i + 1$ is reducible to choice for convex sets in dimension $j$, which in turn is reducib...

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ISBN: 978-3-030-14811-9 978-3-030-14812-6 0302-9743 1611-3349 Japan 15th Annual Conference, TAMC 2019, Kitakyushu, Japan, April 13–16, 2019 2019 https://cronfa.swan.ac.uk/Record/cronfa49944 No Tags, Be the first to tag this record!
Abstract: We study the Weihrauch degrees of closed choice for finite sets, closed choice for convex sets and sorting infinite sequences over finite alphabets. Our main result is that choice for finite sets of cardinality $i + 1$ is reducible to choice for convex sets in dimension $j$, which in turn is reducible to sorting infinite sequences over an alphabet of size $k + 1$, iff $i \leq j \leq k$. Our proofs invoke Kleene's recursion theorem, and we describe in some detail how Kleene's recursion theorem gives rise to a technique for proving separations of Weihrauch degrees. College of Science 378