On the Sensitivity of Cyclically-Invariant Boolean Functions
| dc.creator | Chakraborty, Sourav | |
| dc.date | 2005-01-13 | |
| dc.date.accessioned | 2026-07-07T03:22:21Z | |
| dc.date.available | 2026-07-07T03:22:21Z | |
| dc.description | In this paper we construct a cyclically invariant Boolean function whose sensitivity is $Θ(n^{1/3})$. This result answers two previously published questions. Turán (1984) asked if any Boolean function, invariant under some transitive group of permutations, has sensitivity $Ω(\sqrt{n})$. Kenyon and Kutin (2004) asked whether for a ``nice'' function the product of 0-sensitivity and 1-sensitivity is $Ω(n)$. Our function answers both questions in the negative. We also prove that for minterm-transitive functions (a natural class of Boolean functions including our example) the sensitivity is $Ω(n^{1/3})$. Hence for this class of functions sensitivity and block sensitivity are polynomially related. | |
| dc.identifier | https://arxiv.org/abs/cs/0501026 | |
| dc.identifier | http://arxiv.org/abs/cs/0501026 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/32563 | |
| dc.subject | Computational Complexity | |
| dc.title | On the Sensitivity of Cyclically-Invariant Boolean Functions | |
| dc.type | text |