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Minimization of many-valued functions in a system that includes all one-place functions

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Cybernetics Aims and scope

Summary

The minimization method described here is based on the assumption that there exists either elements that realize all one-place functions, or a method for synthesis of an element that realizes any K-valued function of one independent variable. In either case, the complexity of the elements must not exceed a specified limit, which can be, for example, the complexity of the elements that realize the two-place operations of the chosen base system.

The outstanding feature of the method is the combination of simplicity of synthesis with simplicity of the final cirucits, especially under the spatial principle of information representation, when any K-valued function can be realized exclusively with AND and OR elements.

In addition, the results again confirm the solid foundation of constructions based on the assumption that the processing times of a unit of information in different alphabets are equal.

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Literature Cited

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Authors
  1. A. M. Romankevich
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Additional information

Kiev Polytechnic Institute. Translated from Kibernetika, Vol. 5, No. 3, pp. 49–51, May–June, 1969.

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Romankevich, A.M. Minimization of many-valued functions in a system that includes all one-place functions. Cybern Syst Anal 5, 297–299 (1969). https://doi.org/10.1007/BF01070916

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  • DOI: https://doi.org/10.1007/BF01070916

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