Query complexity of Boolean functions on the middle slice of the cube
We study the query complexity on slices of Boolean functions. Among other results we show that there exists a Boolean function for which we need to query all but 7 input bits to compute its value, even if we know beforehand that the number of 0’s and 1’s in the input are the same, i.e., when our input is from the middle slice. This answers a question of Byramji. Our proof is non-constructive, but we also propose a concrete candidate function that might have the above property. Our results are related to certain natural discrepancy type questions that, somewhat surprisingly, have not been studied before.
Authors
- Gábor Wiener (ORCID: https://orcid.org/0000-0002-3940-3144)
- Balázs Patkós (ORCID: https://orcid.org/0000-0002-1651-2487)
- Kartal Nagy (ORCID: https://orcid.org/0000-0002-9504-7551)
- Dániel Gerbner (ORCID: https://orcid.org/0000-0001-7080-2883)
- Balázs Keszegh (ORCID: https://orcid.org/0000-0002-3839-5103)
- Dömötör Pálvölgyi (ORCID: https://orcid.org/0000-0003-2970-0943)
- Dániel T. Nagy (ORCID: https://orcid.org/0000-0001-6154-7905)
Publication Details
- Journal
- Discrete Applied Mathematics
- Published
- 2024-11-20
- DOI
- https://doi.org/10.1016/j.dam.2024.11.018
- Primary Topic
- Advanced Graph Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Magyar Tudományos Akadémia
- Nemzeti Kutatási Fejlesztési és Innovációs Hivatal
- European Research Council
- Nemzeti Kutatási, Fejlesztési és Innovaciós Alap
- National Research, Development and Innovation Office
- H2020 European Research Council