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Game characterizations and lower cones in the Weihrauch degrees
Logical Methods in Computer Science, Volume: 15, Issue: 3, Pages: 1 - 29
Swansea University Author:
Arno Pauly
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DOI (Published version): 10.23638/LMCS-15(3:11)2019
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...
| Published in: | Logical Methods in Computer Science |
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| ISSN: | 1860-5974 |
| Published: |
2019
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| Online Access: |
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| 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. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
3 |
| Start Page: |
1 |
| End Page: |
29 |