On the search of optimal order of variables in the synthesis of switching circuits by cascade technique Original Research Article

A method is offered of transforming switching circuits built by cascade technique with different order of choice of variables to each other. Based on it, an algorithm is created searching the optimal order of choice of variables for the synthesis of switching circuits by cascade technique; this algorithm is more efficient than the independent synthesis of circuits for each order of variables. Creating the algorithm required solving the following problem: find a sequence x1,x2,…,xn!−1 of permutations xi of n variables consisting of cycles of the form (1,2,…,k), such that all the n! products ∏i=1mxi, m=0,1,…,n!−1, are distinct.