2023/09/24 by Dániel Gerbner, Gerbner, Dániel, Balázs Keszegh +11
Computer Science · #Algorithms and Data Compression #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2309.13678
openalex publication_date 2023/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.