Improved technology mapping for PAL-based devices using a new approach to multi-output boolean functions

2003 ◽  
Author(s):  
D. Kania
Keyword(s):  
Boolean Functions ◽  
Technology Mapping ◽  
New Approach ◽  
Improved Technology

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. 

scholarly journals MogaMap2: Multi-Objective Mapping Algorithm with parameter control for Optimize Area, Performance and Power Consumption in FPGA

2015 ◽  
Vol 10 (2) ◽  
pp. 91-102
Author(s):  
V. L. Souza ◽  
A. G. Silva Filho
Keyword(s):  
Power Consumption ◽  
State Of The Art ◽  
New Technology ◽  
Hybrid Approach ◽  
Parameter Control ◽  
Technology Mapping ◽  
New Approach ◽  
Mapping Algorithm ◽  
Mutation Probability ◽  
Operation Frequency

This article presents a new technology mapper, MogaMap2, the second generation of the technology mapper, MogaMap, based on a hybrid approach that use evolutionary algorithm associated with specific heuristics of the problem in order to find better trade-off results among area, performance and power consumption. Different from MogaMap, the new approach includes a deterministic parameter control that, during the process, modifies the mutation probability. In a set of 20 large designs, we find that this adjust of parameter allow to reduce, in average, the LUT count in 2% and the edge count in 4%. In comparison to state-of-the-art technology mapping, our approach is able to reduce the LUT counts in 3% and the edges count in 10%. Placing and routing the resulting netlists leads to an 3% reduction in the complex logic blocks count, a 7% increasing in estimated operation frequency and 8% reduction in energy consumption.

scholarly journals A Generalized If-Then-Else Operator for the Representation of Multi-Output Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Ilya Levin ◽  
Osnat Keren
Keyword(s):  
Boolean Functions ◽  
Compact Representation ◽  
Decomposition Problem ◽  
New Approach

The paper deals with fundamentals of systems of Boolean functions called multi-output functions (MOFs). A new approach to representing MOFs is introduced based on a Generalized If-Then-Else (GITE) function. It is shown that known operations on MOFs may be expressed by a GITE function. The GITE forms the algebra of MOFs. We use the properties of this algebra to solve an MOF-decomposition problem. The solution provides a compact representation of MOFs.

Boolean functions as points on the hypersphere in the Euclidean space

2019 ◽  
Vol 29 (2) ◽  
pp. 89-101 ◽  
Author(s):  
Oleg A. Logachev ◽  
Sergey N. Fedorov ◽  
Valerii V. Yashchenko
Keyword(s):  
Euclidean Space ◽  
Boolean Function ◽  
Boolean Functions ◽  
Nonlinear Functions ◽  
New Approach ◽  
Injective Mapping

Abstract A new approach to the study of algebraic, combinatorial, and cryptographic properties of Boolean functions is proposed. New relations between functions have been revealed by consideration of an injective mapping of the set of Boolean functions onto the sphere in a Euclidean space. Moreover, under this mapping some classes of functions have extremely regular localizations on the sphere. We introduce the concept of curvature of a Boolean function, which characterizes its proximity (in some sense) to maximally nonlinear functions.

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