Single test for closed contacts in block circuits (Q1094392)

The problem of unique minimal closure test is studied for serial block schemes with contacts of the form \(B^{1,2}\), \(B^{2,2},\ldots, B^{2,2}\), \(B^{2,1}\) where \(B^{i,j}\) is a block having \(i\) inputs and \(j\) outputs. It is assumed that each block contains the contacts of a unique relay, all the relays are distinct and the blocks of a scheme are the simplest (regarding the number of contacts) representatives of equivalent block classes, the number of these classes being equal to 18. In theorems 1--3 lower and upper bounds of minimal test length are deduced for schemes having blocks belonging to some particular classes, and theorem 4 gives the order of minimal test length for any scheme of the assumed structure.