Induced subgraphs of hypercubes and a proof of the sensitivity conjecture
H Huang - Annals of Mathematics, 2019 - projecteuclid.org
In this paper, we show that every (2^n-1+1)-vertex induced subgraph of the n-dimensional
cube graph has maximum degree at least n. This is the best possible result, and it improves …
cube graph has maximum degree at least n. This is the best possible result, and it improves …
Boolean nested canalizing functions: A comprehensive analysis
Boolean network models of molecular regulatory networks have been used successfully in
computational systems biology. The Boolean functions that appear in published models tend …
computational systems biology. The Boolean functions that appear in published models tend …
Sensitivity versus certificate complexity of boolean functions
Sensitivity, block sensitivity and certificate complexity are basic complexity measures of
Boolean functions. The famous sensitivity conjecture claims that sensitivity is polynomially …
Boolean functions. The famous sensitivity conjecture claims that sensitivity is polynomially …
[PDF][PDF] New separation between and
arxiv:1108.3494v1 [cs.CC] 17 Aug 2011 Page 1 arxiv:1108.3494v1 [cs.CC] 17 Aug 2011 New
separation between s(f) and bs(f) Andris Ambainis∗ **aoming Sun† Abstract In this note we …
separation between s(f) and bs(f) Andris Ambainis∗ **aoming Sun† Abstract In this note we …
On the sensitivity conjecture for disjunctive normal forms
S Tavenas - arxiv preprint arxiv:1607.05189, 2016 - arxiv.org
The sensitivity conjecture of Nisan and Szegedy [CC'94] asks whether for any Boolean
function $ f $, the maximum sensitivity $ s (f) $, is polynomially related to its block sensitivity …
function $ f $, the maximum sensitivity $ s (f) $, is polynomially related to its block sensitivity …
Sensitivity, block sensitivity, and certificate complexity of unate functions and read-once functions
H Morizumi - IFIP International Conference on Theoretical Computer …, 2014 - Springer
Sensitivity, block sensitivity, and certificate complexity are complexity measures for Boolean
functions. In this paper, we prove that these three complexity measures are equal to each …
functions. In this paper, we prove that these three complexity measures are equal to each …
On the sensitivity conjecture
A Tal - … on Automata, Languages, and Programming (ICALP …, 2016 - drops.dagstuhl.de
The sensitivity of a Boolean function f:{0, 1}^ n->{0, 1} is the maximal number of neighbors a
point in the Boolean hypercube has with different f-value. Roughly speaking, the block …
point in the Boolean hypercube has with different f-value. Roughly speaking, the block …
Size of sets with small sensitivity: A generalization of simon's lemma
We study the structure of sets S ⊆ {0, 1\}^ n with small sensitivity. The well-known Simon's
lemma says that any S ⊆ {0, 1\}^ n of sensitivity s must be of size at least 2^ ns. This result …
lemma says that any S ⊆ {0, 1\}^ n of sensitivity s must be of size at least 2^ ns. This result …
A tight lower bound on certificate complexity in terms of block sensitivity and sensitivity
Sensitivity, certificate complexity and block sensitivity are widely used Boolean function
complexity measures. A longstanding open problem, proposed by Nisan and Szegedy 7, is …
complexity measures. A longstanding open problem, proposed by Nisan and Szegedy 7, is …
Sensitivity and block sensitivity of nested canalyzing function
Y Li, JO Adeyeye - arxiv preprint arxiv:1209.1597, 2012 - arxiv.org
Based on a recent characterization of nested canalyzing function (NCF), we obtain the
formula of the sensitivity of any NCF. Hence we find that any sensitivity of NCF is between …
formula of the sensitivity of any NCF. Hence we find that any sensitivity of NCF is between …