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The important problem of recognizing a priori the class of Boolean functions which are never obtainable from a given combinational network under short circuit faults is almost unexplored, primarily due to lack of understanding of the functional and structural factors that influence the fault behavior in the network. In view of this, a new concept of impossible class of faulty functions (ICFF) is introduced in this correspondence. Several intriguing properties of ICFF are uncovered, namely, the undetectability of input bridging faults, the impossibility of the transformation of a fault free function Fo to a subset or superset of Fo, and to other functions belonging to the same P-and N-equivalence classes of Fo, etc. The closure amongst the fan-out-free and unate functions under bridging faults is investigated. The impact of ICFF on the testability of the network is also discussed.