Lower bounds on lengths of complete diagnostic tests for circuits and inputs of circuits

Let DP 1 (n) (D P 0 (n), D P 0,1(n)) be the least length of a complete diagnostic test for the primary inputs of logical circuits implementing Boolean functions in n variables and having constant faults of type 1 (respectively 0, both 0 and 1) on these inputs, DO B; 1(n) (D O B; 0(n), D O B; 0,1(n)) be the least length of a complete diagnostic test for logical circuits consisting of logical gates in a basis B, implementing Boolean functions in n variables, and having constant faults of type 1 (respectively 0, both 0 and 1) on outputs of the logical gates, and B2 = {x|y}, B∗ 2 = {x ↑ y}, B3 = {x&y, x}, B∗ 3 = {x ∨ y, x}. It is shown that the functions DP 1 (n), DP 0 (n), DO B2; 1(n), D O B∗ 2 ; 0 (n), DO B3; 0,1(n), D O B∗ 3 ; 0,1 (n) are not less than 2n/2 · 4 √ n