scholarly journals Communication Lower Bounds via Critical Block Sensitivity

2018 ◽  
Vol 47 (5) ◽  
pp. 1778-1806 ◽  
Author(s):  
Mika Göös ◽  
Toniann Pitassi
Keyword(s):  
Lower Bounds ◽  
Block Sensitivity

scholarly journals All Classical Adversary Methods Are Equivalent for Total Functions

2021 ◽  
Vol 13 (1) ◽  
pp. 1-20
Author(s):  
Andris Ambainis ◽  
Martins Kokainis ◽  
Krišjānis Prūsis ◽  
Jevgēnijs Vihrovs ◽  
Aleksejs Zajakins
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Kolmogorov Complexity ◽  
Partial Function ◽  
Query Complexity ◽  
Partial Functions ◽  
Complexity Bound ◽  
Block Sensitivity

We show that all known classical adversary lower bounds on randomized query complexity are equivalent for total functions and are equal to the fractional block sensitivity fbs( f ). That includes the Kolmogorov complexity bound of Laplante and Magniez and the earlier relational adversary bound of Aaronson. This equivalence also implies that for total functions, the relational adversary is equivalent to a simpler lower bound, which we call rank-1 relational adversary. For partial functions, we show unbounded separations between fbs( f ) and other adversary bounds, as well as between the adversary bounds themselves. We also show that, for partial functions, fractional block sensitivity cannot give lower bounds larger than √ n ⋅ bs( f ), where n is the number of variables and bs( f ) is the block sensitivity. Then, we exhibit a partial function f that matches this upper bound, fbs( f ) = Ω (√ n ⋅ bs( f )).

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

Lower bounds on the dimension of the Rauzy gasket

2020 ◽  
Vol 148 (2) ◽  
pp. 321-327
Author(s):  
Rodolfo Gutiérrez-Romo ◽  
Carlos Matheus
Keyword(s):  
Lower Bounds

A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

10.37236/1188 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ramsey Numbers

For $k \geq 5$, we establish new lower bounds on the Schur numbers $S(k)$ and on the k-color Ramsey numbers of $K_3$.

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