Technology mapping techniques for determining whether a function can be implemented using an incomplete lookup table (LUT) are provided. For example, the output of a function is compared to the output of an incomplete LUT for each binary value of the function's input signals and for each binary value of the bits stored in the incomplete LUT. For a LUT that is functionally asymmetric, the process can be repeated for multiple permutations of the input signals with respect to the input terminals of the LUT. As another example, the user function is converted into a network of multiplexers and complete LUTs, which are analyzed to determine if an incomplete LUT can implement the function. As another example, a truth table is constructed for a function. The truth table variables are then tested one by one as candidates for each input position using co-factoring and dependency checking.