Lower bounds for monotone complexity of Boolean functions

1990 ◽  
pp. 75-84 ◽  
Author(s):  
A. A. Razborov
Keyword(s):  
Lower Bounds ◽  
Boolean Functions

Lower Bounds on Formula Size of Boolean Functions Using Hypergraph Entropy

1995 ◽  
Vol 8 (4) ◽  
pp. 536-542 ◽  
Author(s):  
Ilan Newman ◽  
Avi Wigderson
Keyword(s):  
Lower Bounds ◽  
Boolean Functions

scholarly journals Lower bounds to the complexity of symmetric Boolean functions

1990 ◽  
Vol 74 (3) ◽  
pp. 313-323 ◽  
Author(s):  
L. Babai ◽  
P. Pudlák ◽  
V. Rödl ◽  
E. Szemeredi
Keyword(s):  
Lower Bounds ◽  
Boolean Functions ◽  
Symmetric Boolean Functions

On the lower bounds of the second order nonlinearities of some Boolean functions

2010 ◽  
Vol 180 (2) ◽  
pp. 266-273 ◽  
Author(s):  
Sugata Gangopadhyay ◽  
Sumanta Sarkar ◽  
Ruchi Telang
Keyword(s):  
Lower Bounds ◽  
Boolean Functions ◽  
Second Order

scholarly journals Lower bounds for testing triangle-freeness in Boolean functions

2014 ◽  
Vol 24 (1) ◽  
pp. 65-101 ◽  
Author(s):  
Arnab Bhattacharyya ◽  
Ning Xie
Keyword(s):  
Lower Bounds ◽  
Boolean Functions

scholarly journals On a hierarchy of Boolean functions hard to compute in constant depth

2001 ◽  
Vol Vol. 4 no. 2 ◽  
Author(s):  
Anna Bernasconi
Keyword(s):  
Harmonic Analysis ◽  
Complexity Theory ◽  
Lower Bounds ◽  
Boolean Functions ◽  
Combinatorial Property ◽  
Constant Depth ◽  
Models Of Computation ◽  
Mathematical Properties ◽  
International Audience ◽  
Mathematical Techniques

International audience Any attempt to find connections between mathematical properties and complexity has a strong relevance to the field of Complexity Theory. This is due to the lack of mathematical techniques to prove lower bounds for general models of computation.\par This work represents a step in this direction: we define a combinatorial property that makes Boolean functions ''\emphhard'' to compute in constant depth and show how the harmonic analysis on the hypercube can be applied to derive new lower bounds on the size complexity of previously unclassified Boolean functions.

ONE SUFFICIENT AND NECESSARY CONDITION ON BALANCED BOOLEAN FUNCTIONS WITH σf = 22n + 2n+3(n ≥ 3)

2014 ◽  
Vol 25 (03) ◽  
pp. 343-353 ◽  
Author(s):  
YU ZHOU ◽  
LIN WANG ◽  
WEIQIONG WANG ◽  
XINFENG DONG ◽  
XIAONI DU
Keyword(s):  
Lower Bound ◽  
Boolean Function ◽  
Lower Bounds ◽  
Boolean Functions ◽  
Sum Of Squares ◽  
Necessary Condition ◽  
Resilient Function ◽  
The Absolute ◽  
Global Avalanche Characteristics ◽  
Sufficient And Necessary Condition

The Global Avalanche Characteristics (including the sum-of-squares indicator and the absolute indicator) measure the overall avalanche characteristics of a cryptographic Boolean function. Son et al. (1998) gave the lower bound on the sum-of-squares indicator for a balanced Boolean function. In this paper, we give a sufficient and necessary condition on a balanced Boolean function reaching the lower bound on the sum-of-squares indicator. We also analyze whether these balanced Boolean functions exist, and if they reach the lower bounds on the sum-of-squares indicator or not. Our result implies that there does not exist a balanced Boolean function with n-variable for odd n(n ≥ 5). We conclude that there does not exist a m(m ≥ 1)-resilient function reaching the lower bound on the sum-of-squares indicator with n-variable for n ≥ 7.

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