Modular decomposition of the NOR-TSUM multiple-valued PLA

A method for designing PLA-based combinational circuits by modular decomposition is presented. Main subjects are 1) Specific properties of TSUM operator, 2) MIN-TSUM and NOR-TSUM expansions with respect to the bound set, X1 of variables, 3) Realization of functions by multiple-valued PLA-based combinational circuits, 4) Comparison with other methods. Experimental investigations show that the size of suggested combinational circuit is the same as the size of multiple-valued PLA implementing a multiple-valued logic function with large number of variables

On recognition of symmetries for switching functions in Reed-Muller forms

This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. As such, it is in the public domain, and under the provisions of Title 17, United States Code, Section 105, may not be copyrighted.Pattern Recognition and Information Processing, 18-20 May 1999, Minsk, Belarus, 1998This paper addresses the recognition of partial symmetry in variables of switching functions represented in positive polarity Reed-Muller (RM) form. We develop a formal representation of partial symmetries in this RM form and present algorithms for their detection. In addition, we show necessary and sufficient conditions to recognize in RM expression partial and total symmetries in variables of the function. Our program RECsym successfully recognized symmetries in RM expansion in standard benchmark circuits

Development of Zakrevskij's minimization strategy towards arithmetical polynomial domain

In this paper we study the possibility of using the called staircase strategy, originally presented by Zakrevskij, for minimization Boolean function in Arithmetical Polynomials forms. The results on developing staircase minimization strategy to find a quasi-optimal Arithmetical Polynomial forms for both completely and incompletely specified Boolean functions is presented. The experimental results for benchmarks and the comparison with well-known minimization strategies are discussed. 1