PreprintCC BY-NC-SA 4.0arXiv
From raw Solvability Complexity Index proofs to Weihrauch degrees
Abstract
The Solvability Complexity Index (SCI) provides an extensional limit-height formalism for recovering a target map Ξ from finite samples of an evaluation interface Λ by finite-height towers of pointwise limits. At first sight this sounds like a typical Type-2 question, so it seems natural to ask how deep and rich the connection of SCI approximation questions and Type-2 computability questions is. This note aims to explain this connection further with explicit examples mostly from the literature.
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BibTeX
@misc{sorg2026from,
title = {{From raw Solvability Complexity Index proofs to Weihrauch degrees}},
author = {Christopher Sorg},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20378},
eprint = {2609.20378},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20378},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - From raw Solvability Complexity Index proofs to Weihrauch degrees
AU - Christopher Sorg
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20378
UR - https://arxiv.org/abs/2609.20378
AB - The Solvability Complexity Index (SCI) provides an extensional limit-height formalism for recovering a target map Ξ from finite samples of an evaluation interface Λ by finite-height towers of pointwise limits. At first sight this sounds like a typical Type-2 question, so it seems natural to ask how deep and rich the connection of SCI approximation questions and Type-2 computability questions is. This note aims to explain this connection further with explicit examples mostly from the literature.
ER -