Conditions for detecting a logical element fault in a combination device under concurrent checking based on Berger's code

We formulate necessary and sufficient conditions for detecting a fault at the output of a logical element in a combination logical device in a concurrent error-detection system based on Berger's code. We introduce the notion of a fully testable fault. We show that in order to ensure that all single faults in combination devices are detected with their concurrent checking based on Berger's code we can use not only the property that it detects 100 % of unidirectional errors but also the property that it detects 100 % of asymmetrical errors. Due to the latter property, we can reduce structural redundancy of the combination device, when transforming its circuit to one amenable for control, compared to known algorithms for modifying the structure of combination devices into circuits with unidirectionally independent outputs.