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Game Characterizations and Lower Cones in the Weihrauch Degrees

  • Hugo Nobrega
  • Arno Pauly
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10307)

Abstract

We introduce generalized Wadge games and show that each lower cone in the Weihrauch degrees is characterized by such a game. These generalized Wadge games subsume (a variant of) 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 generalized Wadge games.

Notes

Acknowledgments

We are grateful to Benedikt Löwe, Luca Motto Ros, Takayuki Kihara and Raphaël Carroy for helpful and inspiring discussions. We would also like to thank the anonymous referees for the many corrections which have significantly improved the paper.

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Copyright information

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Authors and Affiliations

  1. 1.Institute for Logic, Language, and ComputationUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Département D’informatiqueUniversité Libre de BruxellesBrusselsBelgium

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