Year: 2026
Type: preprint
Abstract: We study block sensitivity and certificate complexity of rotation symmetric Boolean functions, with particular emphasis on monomial rotation symmetric Boolean functions. We first show that every odd-degree monomial rotation symmetric Boolean function on $n$ variables satisfies $s=bs=C=n$. We then determine sensitivity, block sensitivity, and certificate complexity for every quadratic monomial rotation symmetric Boolean function. For the quadratic function $Q_{n,k}$ generated by $x_0x_k$, we prove, outside the short-orbit case, that \[ C(Q_{n,k})= \begin{cases} n,&4\mid n/\gcd(n,k),\\ n-\gcd(n,k),&4\nmid n/\gcd(n,k). \end{cases} \] Moreover, \(bs(Q_{n,k})=C(Q_{n,k})\) for every quadratic MRS function, and outside the short-orbit case, strict separation \(s
Source: arXiv (Cornell University)
Authors: Li, Yuan, Zhang, Jing
Institutions: Winston-Salem State University, Governors State University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221794983