A spectral characterization of the self-dualized classification of boolean functions

1986 ◽  
Vol 61 (1) ◽  
pp. 65-72 ◽  
Author(s):  
D. M. MILLER ◽  
J. C. MUZIO
2015 ◽  
Vol 28 (1) ◽  
pp. 51-76 ◽  
Author(s):  
Bernd Steinbach ◽  
Christian Posthoff

The Boolean Differential Calculus (BDC) significantly extends the Boolean Algebra because not only Boolean values 0 and 1, but also changes of Boolean values or Boolean functions can be described. A Boolean Differential Equation (BDe) is a Boolean equation that includes derivative operations of the Boolean Differential Calculus. This paper aims at the classification of BDEs, the characterization of the respective solutions, algorithms to calculate the solution of a BDe, and selected applications. We will show that not only classes and arbitrary sets of Boolean functions but also lattices of Boolean functions can be expressed by Boolean Differential equations. In order to reach this aim, we give a short introduction into the BDC, emphasize the general difference between the solutions of a Boolean equation and a BDE, explain the core algorithms to solve a BDe that is restricted to all vectorial derivatives of f (x) and optionally contains Boolean variables. We explain formulas for transforming other derivative operations to vectorial derivatives in order to solve more general BDEs. New fields of applications for BDEs are simple and generalized lattices of Boolean functions. We describe the construction, simplification and solution. The basic operations of XBOOLE are sufficient to solve BDEs. We demonstrate how a XBooLe-problem program (PRP) of the freely available XBooLe-Monitor quickly solves some BDes.


2002 ◽  
Vol 7 (4) ◽  
pp. 245-255 ◽  
Author(s):  
Adrian Furnham ◽  
Thomas Li-Ping Tang ◽  
David Lester ◽  
Rory O'Connor ◽  
Robert Montgomery

A total of 253 British and 318 American students were asked to make various estimates of overall intelligence as well as Gardner's (1999a) new list of 10 multiple intelligences. They made these estimations (11 in all) for themselves, their partner, and for various well-known figures such as Prince Charles, Tony Blair, Bill Gates, and Bill Clinton. Following previous research there were various sex and nationality differences in self-estimated IQ: Males rated themselves higher on verbal, logical, spatial, and spiritual IQ compared to females. Females rated their male partner as having lower verbal and spiritual, but higher spatial IQ than was the case when males rated their female partners. Participants considered Bill Clinton (2 points) and Prince Charles (5 points) less intelligent than themselves, but Tony Blair (5 points) and Bill Gates (15 points) more intelligent than themselves. Multiple regressions indicated that the best predictors of one's overall IQ estimates were logical, verbal, existential, and spatial IQ. Factor analysis of the 10 and then 8 self-estimated scores did not confirm Gardner's classification of multiple intelligences. Results are discussed in terms of the growing literature in the self-estimates of intelligence, as well as limitations of that approach.


2014 ◽  
Vol 59 (3) ◽  
pp. 313-318
Author(s):  
C. Cheptea ◽  
◽  
L.M. Ivan ◽  
D.O. Dorohoi ◽  
V. Sunel ◽  
...  

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