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The spectral test of the Boolean function linearity

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Porwik P.

International Journal of Applied Mathematics and Computer Science

2003

tom 13

nr 4

567-575

The paper discusses the problem of recognizing the Boolean function linearity. A spectral method of the analysis of Boolean functions using the Walsh transform is described. Linearity and nonlinearity play important roles in the design of digital circuits. The analysis of the distribution of spectral coefficients allows us to determine various combinatorial properties of Boolean functions, such as redundancy, monotonicity, self-duality, correcting capability, etc., which seems more difficult be performed by means of other methods. In particular, the basic synthesis method described in the paper allows us to compute the spectral coefficients in an iterative manner. The method can be easily used in investigations of large Boolean functions (of many variables), which seems very attractive for modern digital technologies. Experimental results demonstrate the efficiency of the approach.

WWW-based Boolean function minimization

100%

Tomaszewski S. P., Celik I. U., Antoniou G. E.

International Journal of Applied Mathematics and Computer Science

2003

tom 13

nr 4

577-583

In this paper a Boolean minimization algorithm is considered and implemented as an applet in Java. The application is based on the Quine-McCluskey simplification technique with some modifications. The given application can be accessed on line since it is posted on the World Wide Web (WWW), with up to four variables, at the URL http://www.csam.montclair.edu/~antoniou/bs. After extensive testing, the performance of the algorithm has been found to be excellent. The proposed application is a useful aid for students and professors in the fields of electrical and computer engineering and computer science as well as a valuable tool for digital designers.

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

1 Antoniou G. E.

1 Celik I. U.

1 Porwik P.

1 Tomaszewski S. P.

2 2003

Wyniki wyszukiwania

The spectral test of the Boolean function linearity

WWW-based Boolean function minimization