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1

Signature pre - procesing based on walsh coefficients

Porwik P., Wróbel K.

Journal of Medical Informatics & Technologies

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2008

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Vol. 12

57--61

EN

Recognition and verification of persons are difficult and important tasks today. In many fields of human activities (driver's licenses, passports, electronic cards, etc.), signature recognition of person is needed. Hence, it inspires the development of a wide range of automatic identification systems. Signatures have been used for many centuries as a method of people's identification. Signatures recognition was performed manually by experts in the past. Nowadays, these procedures are very often automatically applied. In this paper the system that automatically authenticates documents based on the owner's handwritten signature is presented.

2

Efficient Algorithm of Affine form Searching for Weakly Specified Boolean Function

Porwik P.

Fundamenta Informaticae

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2007

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Vol. 77, nr 3

277-291

EN

This paper presents the spectral method of recognition of an incompletely defined Boolean function. The main goal of analysis is fast estimation whether a given single output function can be extended to affine form. Furthermore, a simple extension algorithm is proposed for functions, for which the affine form is reachable. The algorithm is compared with other methods. Theoretical and experimental results demonstrate the efficiency of the presented approach.

3

Efficient spectral method of identification of linear Boolean function

Porwik P.

Control and Cybernetics

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2004

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Vol. 33, no 4

663-678

EN

This paper discusses a problem of recognition of the Boolean function's linearity. The article describes the spectral method of analysis of incompletely specified Boolean functions using the Walsh Transform. The linearity and nonlinearity play an important role in design of digital circuits. The analysis of the spectral coefficients' distribution allows to determine the various combinatorial properties of the Boolean functions: redundancy, monotonicity, self-duality, correcting capability, etc. which seems to be more difficult to obtain by means of other methods. In particular, the distribution of spectral coefficients allows us to determine whether Boolean function is linear. The method described in the paper can be easily used in investigations of large Boolean functions (of many variables), what seems to be very attractive for modern digital technologies. Experimental results demonstrate the efficiency of the approach.

4

The Spectral Test of the Boolean Function Linearity

Porwik P.

International Journal of Applied Mathematics and Computer Science

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2003

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Vol. 13, no 4

567-575

EN

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.

5

Efficient Calculation of the Reed-Muller Form by Means of the Walsh Transform

Porwik P.

International Journal of Applied Mathematics and Computer Science

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2002

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Vol. 12, no 4

571-579

EN

The paper describes a spectral method for combinational logic synthesis using the Walsh transform and the Reed-Muller form. A new algorithm is presented that allows us to obtain the mixed polarity Reed-Muller expansion of Boolean functions. The most popular minimisation (sub-minimisation) criterion of the Reed-Muller form is obtained by the exhaustive search of all the polarity vectors. This paper presents a non-exhaustive method for Reed-Muller expansions. The new method allows us to build the Reed-Muller form based on the analysis of Walsh-Hadamard coefficients. The presented method has much less complexity than the procedures which have been applied until now. Both the transforms and the presented Walsh-Hadamard spectral characterization of the Reed-Muller expansion are compared. An analysis of the properties of the spectra obtained from these transforms is made.