Lower bounds for Sum and Sum of Products of Read-once Formulas

2019 ◽  
Vol 11 (2) ◽  
pp. 1-27 ◽  
Author(s):  
C. Ramya ◽  
B. V. Raghavendra Rao
Keyword(s):  
Lower Bounds ◽  
Sum Of Products

An Asymptotic Formula for a Sum of Products of Powers

1978 ◽  
Vol 21 (4) ◽  
pp. 427-433
Author(s):  
Ronald J. Evans
Keyword(s):  
Asymptotic Formula ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Sum Of Products ◽  
Image Position

Fix an integer r ≥ 2 and positive numbers b1, …, br. Write σ = b1+ …+br Let . In this note we evaluate the constant A (when it exists) for which1where the sum is over all vectors2We also obtain upper and lower bounds for the sum in (1).

scholarly journals EXACT MINIMIZATION OF AND–EXOR EXPRESSIONS OF PRACTICAL BENCHMARK FUNCTIONS

2009 ◽  
Vol 18 (03) ◽  
pp. 465-486 ◽  
Author(s):  
TAKASHI HIRAYAMA ◽  
YASUAKI NISHITANI
Keyword(s):  
Lower Bounds ◽  
Search Space ◽  
Computing Methods ◽  
Experimental Results ◽  
Upper And Lower Bounds ◽  
Search Procedure ◽  
Minimization Algorithm ◽  
Original Algorithm ◽  
Sum Of Products ◽  
Exclusive Or

We propose faster-computing methods for the minimization algorithm of AND–EXOR expressions, or exclusive-or sum-of-products expressions (ESOPs), and obtain the exact minimum ESOPs of benchmark functions. These methods improve the search procedure for ESOPs, which is the most time-consuming part of the original algorithm. For faster computation, the search space for ESOPs is reduced by checking the upper and lower bounds on the size of ESOPs. Experimental results to demonstrate the effectiveness of these methods are presented. The exact minimum ESOPs of many practical benchmark functions have been revealed by this improved algorithm.

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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