Query complexity of Boolean functions on the middle slice of the cube

Year: 2024

Type: article

Abstract: 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.

Source: Discrete Applied Mathematics

DOI: 10.1016/j.dam.2024.11.018

Authors: Dániel Gerbner, Balázs Keszegh, Dániel T. Nagy, Kartal Nagy, Dömötör Pálvölgyi, Balázs Patkós, Gábor Wiener

Institutions: HUN-REN Alfréd Rényi Institute of Mathematics, Hungarian Research Network, Eötvös Loránd University, Budapest University of Technology and Economics

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,860

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

OpenAlex ID: W4404541123