KGPMAP: library-based technology-mapping technique for antifuse based FPGAs

S. Chattopadhyay et al. (1994) recently proposed a signature based library search mapper that is able to distinguish the nonequivalent functions with very low aliasing. The method uses an algebraic transformation of Boolean functions into the corresponding polynomial form and then characterises the polynomial by means of prime numbers. While the technique is very interesting the algebraic transform used in the method has been introduced before. Hence the claim in the article that the new transform matrix is introduced is incorrect. The authors correctly state that the transform used is related to a similar transform with different handling of the negation. This similar transform is known under different names and has been investigated by different authors. It is found under the names of `probabilistic transform´, `arithmetic transform´ and `algebraic transform´. The transform matrix of the arithmetic transform is nonsingular and its inverse is formed of all the elements having only entries equal to 1. I propose to use the inverse of the arithmetic transform as the transform on its own in different applications in logic design and name it `adding transform´