Row-shift decompositions for index generation functions

This paper shows a realization of incompletely specified index generation functions in the form f(X
₁
,X
₂
) = g(h(X
₁
)+X
₂
), where + denotes an integer addition. A decomposition algorithm is shown. Experimental results show that most of n = 2q-3 variable functions where k = 2
^q
-1 combinations are specified can be realized by a pair of q-input q-output LUTs. The computation time is O(k). Experimental results using address tables, lists of English words, and randomly generated functions are shown.