EXORCISM-MV-2: minimization of exclusive sum of products expressions for multiple-valued input incompletely specified functions

A cube operation, EXORLINK, and its application to the minimization of multiple-valued input, multi-output exclusive sums of products (ESOPs) for incompletely specified Boolean functions, are presented. EXORLINK generalizes all cube operations, such as crosslink, unlink, and X-merge. The authors' program, EXORCISM-MV-2, gives efficient results for functions that are incompletely specified and have an arbitrary number of values for each of the input variables. This allows realization of a wider class of circuits that implement the multiple-valued input ESOP expressions. Evaluation on benchmark functions is also given and proves the superiority of the program to those known from the literature.<<ETX>>

[1]  P.W. Besslich,et al.  An efficient program for logic synthesis of mod-2 sum expressions , 1991, Euro ASIC '91.

[2]  Tsutomu Sasao,et al.  Minimization of AND-EXOR Expressions Using Rewrite Rules , 1993, IEEE Trans. Computers.

[3]  Marek A. Perkowski,et al.  Multiple-valued generalized Reed-Muller forms , 1991, [1991] Proceedings of the Twenty-First International Symposium on Multiple-Valued Logic.

[4]  John P. Robinson,et al.  A Method for Modulo-2 Minimization , 1982, IEEE Transactions on Computers.

[5]  Tsutomu Sasao.  EXMIN: a simplification algorithm for exclusive-OR-sum-of-products expressions for multiple-valued input two-valued output functions , 1990, Proceedings of the Twentieth International Symposium on Multiple-Valued Logic.

[6]  D. Green.  Reed-Muller canonical forms with mixed polarity and their manipulations , 1990 .

[7]  Xia Chen,et al.  Mapping of Reed-Muller coefficients and the minimisation of exclusive OR-switching functions , 1982 .

[8]  Tsutomu Sasao.  EXMIN2: a simplification algorithm for exclusive-OR-sum-of-products expressions for multiple-valued-input two-valued-output functions , 1993, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[9]  M. Perkowski,et al.  Minimization of multiple-valued input multi-output mixed-radix exclusive sums of products for incompletely specified Boolean functions , 1989, Proceedings. The Nineteenth International Symposium on Multiple-Valued Logic.

[10]  Donald Leo Dietmeyer,et al.  Logic design of digital systems , 1971 .

[11]  Harold Fleisher,et al.  A Computer Algorithm for Minimizing Reed-Muller Canonical Forms , 1987, IEEE Transactions on Computers.

[12]  Marek A. Perkowski,et al.  A fast algorithm to minimize multi-output mixed-polarity generalized Reed-Muller forms , 1988, DAC '88.

[13]  J. M. Saul.  An improved algorithm for the minimization of mixed polarity Reed-Muller representations , 1990, Proceedings., 1990 IEEE International Conference on Computer Design: VLSI in Computers and Processors.

[14]  Dhiraj K. Pradhan,et al.  Fault-tolerant computing : theory and techniques , 1986 .

[15]  P. Besslich.  Efficient computer method for ExOR logic design , 1983 .

[16]  George K. Papakonstantinou.  Minimization of Modulo-2 Sum of Products , 1979, IEEE Transactions on Computers.

[17]  Stephen Y. H. Su,et al.  Computer Minimization of Multivalued Switching Functions , 1972, IEEE Transactions on Computers.

[18]  M. Perkowski,et al.  An exact algorithm to minimize mixed-radix exclusive sums of products for incompletely specified Boolean functions , 1990, IEEE International Symposium on Circuits and Systems.

[19]  Chyan Yang,et al.  Experiences of parallel processing with direct cover algorithms for multiple-valued logic minimization , 1992, [1992] Proceedings The Twenty-Second International Symposium on Multiple-Valued Logic.

[20]  Hideo Fujiwara,et al.  Logic Testing and Design for Testability , 1985 .

[21]  Tsutomu Sasao,et al.  Multiple-Valued Decomposition of Generalized Boolean Functions and the Complexity of Programmable Logic Arrays , 1981, IEEE Transactions on Computers.

[22]  M. Perkowski,et al.  Canonical restricted mixed-polarity exclusive-OR sums of products and the efficient algorithm for their minimisation , 1993 .