A new approach to the decomposition of Boolean functions by the method of q-partitions. III. Joint decomposition of a function system

2007 ◽  
Vol 43 (2) ◽  
pp. 192-207
Author(s):  
B. E. Rytsar
Keyword(s):  
Boolean Functions ◽  
Function System ◽  
New Approach ◽  
Joint Decomposition ◽  
Decomposition Of Boolean Functions

scholarly journals IDENTIFICATION OF BINARY CELLULAR AUTOMATA FROM SPATIO-TEMPORAL BINARY PATTERNS USING A FOURIER REPRESENTATION

2007 ◽  
Vol 17 (06) ◽  
pp. 1985-1996 ◽  
Author(s):  
L. Z. GUO ◽  
S. A. BILLINGS
Keyword(s):  
Fourier Transform ◽  
Cellular Automata ◽  
Least Squares ◽  
Boolean Functions ◽  
Multilinear Polynomial ◽  
Polynomial Representation ◽  
New Approach ◽  
Spatio Temporal ◽  
The Fourier Transform ◽  
Robust To Noise

The identification of binary cellular automata from spatio-temporal binary patterns is investigated in this paper. Instead of using the usual Boolean or multilinear polynomial representation, the Fourier transform representation of Boolean functions is employed in terms of a Fourier basis. In this way, the orthogonal forward regression least-squares algorithm can be applied directly to detect the significant terms and to estimate the associated parameters. Compared with conventional methods, the new approach is much more robust to noise. Examples are provided to illustrate the effectiveness of the proposed approach.

scholarly journals A New Approach to Simplifying Boolean Functions

2004 ◽  
Vol 1 (1) ◽  
pp. 39
Author(s):  
A. H. M. Ashfak Habib ◽  
Md. Abdus Salam ◽  
Zia Nadir ◽  
Hemen Goswami
Keyword(s):  
Boolean Functions ◽  
New Approach ◽  
Manual Method ◽  
The Cost

There are many benefits to simplifying Boolean functions before they are implemented in hardware. A reduced number of gates decreases considerably the cost of the hardware, reduces the heat generated by the chip and, most importantly, increases the speed. But no method is effective for the simplification of Boolean functions, if it involves more than six variables. This paper presents a new manual method of simplification that can be effectively applied to problems with a large number of variables. 

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