The specificity of error detection as part of computing testing in digital devices based on self-duality of Boolean functions

Abstract

Aim. To identify the specificity of error detection as part of self-dual calculations testing by automation devices, as well as to propose a method for organising calculations testing that would allow detecting any malfunctions from the defined model. Methods. The paper used methods of technical diagnostics of discrete systems, Boolean algebra, and combinatorics. Results. The specificity of error detection at the outputs of self-dual digital devices of combination type were analysed. The conditions for detecting and not detecting errors at the outputs of self-dual combinational circuits were formalised. In practice, the latter allow – by analysing potential errors at the outputs – creating fully self-checking circuits. At the same time, it is noted that if full coverage of all errors at the outputs of self-dual circuits cannot be achieved when computing-testing only on the basis of whether a function belongs to the self-dual class, then in some cases that can be made possible through additional checking of whether the generated code vectors belong to a pre-selected redundant code. It is established, what features of actual digital devices enable large numbers of errors compensated for by self-dual testing. It is theoretically determined that, in real practical applications with self-dual computing testing, the larger is the number of input variables, the higher is the probability of not detecting an error due to a larger number of combinations of distortions at the outputs. However, the greater is the number of functions implemented by a device, the higher is the probability of error detection. Nonetheless, in practice, each case of computations testing based on the self-duality of calculated functions should be treated individually for each digital device. The paper presents some experimental results that demonstrate the specificity of error detection at the outputs of self-dual combinational circuits using various circuit design methods based on compressing the signals received from the monitored facilities using modified Hamming codes (Hsiao codes). Conclusion. The conditions for detecting errors at the outputs of self-dual digital devices established in this paper allow practically synthesising self-checking computer systems with improved checkability as compared with conventional approaches to their implementation.