Totally Undecomposable Functions: Applications to Efficient Multiple-Valued Decompositions

A function f : P ! P , P = f0; 1; : : : ; p 1g is kdecomposable i f can be represented as f(X1;X2) = g(h1(X1); h2(X1); : : : ; hk(X1);X2), where (X1; X2) is a bipartition of input variables. This paper introduces the notion of totally k-undecomposable functions. By using this concept, we can drastically reduce the search space to nd k-decompositions. A systematic method to nd the bipartitions of input variables that will not produce any k-decompositions is presented. By combining it to the conventional decomposition methods, we can build an e cient functional decomposition system. This method is promising to design LUT-based FPGAs.