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Game characterizations and lower cones in the Weihrauch degrees / Hugo Nobrega; Arno Pauly

Logical Methods in Computer Science, Volume: 15, Issue: 3, Pages: 1 - 29

Swansea University Author: Arno, Pauly

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Abstract

We introduce a parametrized version of the Wadge game for functions and show that each lower cone in the Weihrauch degrees is characterized by such a game. These parametrized Wadge games subsume the original Wadge game, the eraser and backtrack games as well as Semmes's tree games. In particula...

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Published in: Logical Methods in Computer Science
ISSN: 1860-5974
Published: 2019
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa51342
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Abstract: We introduce a parametrized version of the Wadge game for functions and show that each lower cone in the Weihrauch degrees is characterized by such a game. These parametrized Wadge games subsume the original Wadge game, the eraser and backtrack games as well as Semmes's tree games. In particular, we propose that the lower cones in the Weihrauch degrees are the answer to Andretta's question on which classes of functions admit game characterizations. We then discuss some applications of such parametrized Wadge games. Using machinery from Weihrauch reducibility theory, we introduce games characterizing every (transfinite) level of the Baire hierarchy via an iteration of a pruning derivative on countably branching trees.
College: College of Science
Issue: 3
Start Page: 1
End Page: 29