Short single-fault tests for circuits in the Zhegalkin basis with arbitrary constant faults of gates

The problem of implementing Boolean functions by irredundant Boolean circuits in the Zhegalkin basis which admit short single-fault tests in the presence of arbitrary stuck-at faults at gate outputs is considered. It is proved that the Shannon function of the length of a single-fault fault detection (single-fault diagnostic) test does not exceed $3$ (respectively, $5$).