Further Comments on "Synthesis of Symmetric Switching Functions Using Threshold Logic Networks"1

Recently, Fischler and Tannenbaum²indicated a counter example to Theorem 2 of this author\´s short note.¹Theorem 2 (as well as the other theorems in the note) is a statement of the sufficiency conditions only. This means that if the conditions given in Theorem 2 are satisfied, then it is always possible to find a minimal realization for five positive transitions. It does not say that if the conditions given in Theorem 2 are not fulfilled, it is not possible to obtain such a network. The counterexample is such a case. The author regrets the use of the phrase "necessary and sufficient conditions" in the abstract and elsewhere in the note.¹This should be read as "sufficient conditions only."