Efficient spectral method of identification of linear Boolean function
Efficient calculation of the Reed-Muller form by means of the Walsh transform
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...
The spectral test of the Boolean function linearity
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...
Dedicated spectral method of Boolean function decomposition
Spectral methods constitute a useful tool in the analysis and synthesis of Boolean functions, especially in cases when other methods reduce to brute-force search procedures. There is renewed interest in the application of spectral methods in this area, which extends also to the closely connected concept of the autocorrelation function, for which spectral methods provide fast calculation algorithms. This paper discusses the problem of spectral decomposition of Boolean functions using the Walsh transform...
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