English

A note on the diamond operator

Logic 2020-06-16 v3

Abstract

We show that if 1WF1 \leq_W F and FFWFF \star F \leq_W F, then FWFF^\diamond \leq_W F, where \star and \diamond are the following operations in the Weihrauch lattice: \star is the compositional product, which allows the use of two principles in sequence, while the diamond operator \diamond allows an arbitrary but finite number of uses of the given principle in sequence. This answers a question of Pauly.

Cite

@article{arxiv.2001.09372,
  title  = {A note on the diamond operator},
  author = {Linda Westrick},
  journal= {arXiv preprint arXiv:2001.09372},
  year   = {2020}
}

Comments

5 pages

R2 v1 2026-06-23T13:20:42.460Z