On the synthesis of circuits admitting complete fault detection test sets of constant length under arbitrary constant faults at the outputs of the gates

Abstract

We describe a method of construction of circuits over some special basis admitting complete tests detecting arbitrary constant faults at the outputs of gates and having length not exceeding 4.

Lower bounds for lengths of single tests for Boolean circuits

“…. Romanov in [10] proved that there exists a basis 3 consisting of gates with arity from 1 to 7 such that 2 ; similarly it can be proved that ; , ( ) ≲ 2 , = 0, 1. [11,12] ( ) = 1 [16] (with P. A. Borodin).…”

Method of synthesis of easily testable circuits admitting single fault detection tests of constant length

“…The author of the present paper has put forward [15] two examples of complete bases of functional elementš ὔ , ὔὔ such that ̌ ὔ ( ) ≤ 4. He also showed [16] that in the basiš ὔὔ the Shannon function for the length of a complete fault detection test with respect to arbitrary constant faults at the outputs of the gates is at most 4 for any nonnegative integer . Besides, Noskov [17] has showed that, for each Boolean function (̃ ), in an arbitrary complete basis there exists a circuit with three additional inputs and one additional output such that the function is a subfunction of one of the two functions realized by the circuit , and moreover, the length of a test capable of checking at most arbitrary faults of gates or blocks of the circuit is ( + 2 ).…”