Combinational multiple-valued circuit design by generalised disjunctive decomposition

A design of multiple-valued circuits based on the multiple-valued programmable logic arrays (MV PLA’s) by generalized disjunctive decomposition is presented. Main subjects are 1) Generalized disjunctive decomposition of multiple-valued functions using multiple-terminal multiplevalued decision diagrams (MTMDD’s); 2) Realization of functions by MV PLA-based combinatorial circuits

Genetic algorithm approach to find the best input variable partitioning

Conference PaperThis paper presents a variable partition algorithm which combines the quasi-reduced ordered multiple-terminal multiple-valued decision diagrams and genetic algorithms (GAs). The algorithm is better than the previous techniques which find a good functional decomposition by non-exhaustive search and expands the range of searching for the best decomposition providing the optimal subtable multiplicity. The possible solutions are evaluated using the gain of decomposition for a multiple-output multiple-valued logic function. The distinct feature of GA is the possible solutions being coded by real numbers. Here the simplex-based crossover is proposed to use for the recombination stage of GA. It permits to increase the GA coverag

Time complexity analysis of generalized decomposition algorithm

The time complexity of the fast algorithm for generalized disjunctive decomposition of an rvalued function is studied.The considered algorithm to find the best decomposition is based on the analysis of multiple-terminal multiple-valued decision diagrams. It is shown that the time complexity for random rvalued functions depends on the such restriction as the number n1 of inputs in the first level circuit. In the case where the best partition of input variables is searched with restriction the time complexity is reduced in several times. The algorithm was simulated on a digital computer. The experimental results are in agreement with the theoretical predictions

Using a genetic algorithm for optimizing the functional decomposition of multiple-valued functions

The genetic algorithm which determines the good functional decomposition of multiple-valued logic functions is presented. The algorithm expands the range of searching for a best decomposition, providing the optimal column multiplicity. The possible solutions are evaluated using the gain of decomposition for multiple-valued function

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